Hands On Exercise 3

4.1 Overview

Spatial Point Pattern Analysis is the evaluation of the pattern or distribution, of a set of points on a surface. The point can be location of:

• events such as crime, traffic accident and disease onset, or

• business services (coffee and fastfood outlets) or facilities such as childcare and eldercare.

Using appropriate functions of spatstat, this hands-on exercise aims to discover the spatial point processes of childecare centres in Singapore.

The specific questions we would like to answer are as follows:

• are the childcare centres in Singapore randomly distributed throughout the country?

• if the answer is not, then the next logical question is where are the locations with higher concentration of childcare centres?

4.2 The data

To provide answers to the questions above, three data sets will be used. They are:

• CHILDCARE, a point feature data providing both location and attribute information of childcare centres. It was downloaded from Data.gov.sg and is in geojson format.

• MP14_SUBZONE_WEB_PL, a polygon feature data providing information of URA 2014 Master Plan Planning Subzone boundary data. It is in ESRI shapefile format. This data set was also downloaded from Data.gov.sg.

• CostalOutline, a polygon feature data showing the national boundary of Singapore. It is provided by SLA and is in ESRI shapefile format. (This data needs to be derived ourselves using  st_union or st_combine() and to transform tibble data.frame, we need to use st_transform()

4.3 Installing and Loading the R packages

In this hands-on exercise, five R packages will be used, they are:

• sf, a relatively new R package specially designed to import, manage and process vector-based geospatial data in R.

• spatstat, which has a wide range of useful functions for point pattern analysis. In this hands-on exercise, it will be used to perform 1st- and 2nd-order spatial point patterns analysis and derive kernel density estimation (KDE) layer.

• raster which reads, writes, manipulates, analyses and model of gridded spatial data (i.e. raster). In this hands-on exercise, it will be used to convert image output generate by spatstat into raster format.

• maptools which provides a set of tools for manipulating geographic data. In this hands-on exercise, we mainly use it to convert Spatial objects into ppp format of spatstat.

• tmap which provides functions for plotting cartographic quality static point patterns maps or interactive maps by using leaflet API.

Use the code chunk below to install and launch the five R packages.

install.packages("maptools", repos = "https://packagemanager.posit.co/cran/2023-10-13")

Installing package into 'C:/Users/cedri/AppData/Local/R/win-library/4.3'
(as 'lib' is unspecified)

package 'maptools' successfully unpacked and MD5 sums checked

Warning: cannot remove prior installation of package 'maptools'

Warning in file.copy(savedcopy, lib, recursive = TRUE): problem copying
C:\Users\cedri\AppData\Local\R\win-library\4.3\00LOCK\maptools\libs\x64\maptools.dll
to
C:\Users\cedri\AppData\Local\R\win-library\4.3\maptools\libs\x64\maptools.dll:
Permission denied

Warning: restored 'maptools'

The downloaded binary packages are in
    C:\Users\cedri\AppData\Local\Temp\RtmpSWmA78\downloaded_packages

pacman::p_load(maptools, sf, raster, spatstat, tmap)

4.4 Spatial Data Wrangling

4.4.1 Importing the spatial data

In this section, st_read() of sf package will be used to import these three geospatial data sets into R.

childcare_sf = st_read("data/geospatial/ChildCareServices.geojson") %>%
  st_transform(crs = 3414)

Reading layer `ChildCareServices' from data source 
  `C:\AloysiusCedric\IS415-GAA\Hands-on_Ex\Hands-on_Ex03\data\geospatial\ChildCareServices.geojson' 
  using driver `GeoJSON'
Simple feature collection with 1925 features and 2 fields
Geometry type: POINT
Dimension:     XYZ
Bounding box:  xmin: 103.6878 ymin: 1.247759 xmax: 103.9897 ymax: 1.462134
z_range:       zmin: 0 zmax: 0
Geodetic CRS:  WGS 84

mpsz_sf = st_read(dsn="data/geospatial", layer="MP14_SUBZONE_WEB_PL")%>%
  st_transform(crs=3414)

Reading layer `MP14_SUBZONE_WEB_PL' from data source 
  `C:\AloysiusCedric\IS415-GAA\Hands-on_Ex\Hands-on_Ex03\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21

st_crs(mpsz_sf)

Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]

Combining to get the coastal line

sg_sf = st_union(mpsz_sf)%>%
  st_transform(crs=3414)

#plot(sg_sf)

#sg_sf = st_transform(sg_sf, crs=3414)
plot(sg_sf)

sg_sf

Geometry set for 1 feature 
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21 / Singapore TM

MULTIPOLYGON (((17763.39 15889.1, 17758.6 15868...

st_crs(sg_sf)

Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]

tmap_mode('view')

tmap mode set to interactive viewing

tm_shape(sg_sf) +
  tm_borders("white", lwd = .5) +
  
tm_shape(childcare_sf)+
  tm_dots()

tmap_mode('view')

tmap mode set to interactive viewing

tm_shape(childcare_sf)+
  tm_dots()

tmap_mode('plot')

tmap mode set to plotting

Notice that at the interactive mode, tmap is using leaflet for R API. The advantage of this interactive pin map is it allows us to navigate and zoom around the map freely. We can also query the information of each simple feature (i.e. the point) by clicking of them. Last but not least, you can also change the background of the internet map layer. Currently, three internet map layers are provided. They are: ESRI.WorldGrayCanvas, OpenStreetMap, and ESRI.WorldTopoMap. The default is ESRI.WorldGrayCanvas.

Reminder: Always remember to switch back to plot mode after the interactive map. This is because, each interactive mode will consume a connection. You should also avoid displaying ecessive numbers of interactive maps (i.e. not more than 10) in one RMarkdown document when publish on Netlify.

4.5 Geospatial Data wrangling

Although simple feature data frame is gaining popularity again sp’s Spatial* classes, there are, however, many geospatial analysis packages require the input geospatial data in sp’s Spatial* classes. In this section, you will learn how to convert simple feature data frame to sp’s Spatial* class.

4.5.1 Converting sf data frames to sp’s Spatial* class

The code chunk below uses as_Spatial() of sf package to convert the three geospatial data from simple feature data frame to sp’s Spatial* class.

childcare <- as_Spatial(childcare_sf)
mpsz <- as_Spatial(mpsz_sf)
sg <- as_Spatial(sg_sf)

childcare

class       : SpatialPointsDataFrame 
features    : 1925 
extent      : 11810.03, 45404.24, 25596.33, 49300.88  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
variables   : 2
names       :    Name,                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Description 
min values  :   kml_1, <center><table><tr><th colspan='2' align='center'><em>Attributes</em></th></tr><tr bgcolor="#E3E3F3"> <th>ADDRESSBLOCKHOUSENUMBER</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSBUILDINGNAME</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSPOSTALCODE</th> <td>100044</td> </tr><tr bgcolor=""> <th>ADDRESSSTREETNAME</th> <td>44, TELOK BLANGAH DRIVE, #01 - 19/51, SINGAPORE 100044</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSTYPE</th> <td></td> </tr><tr bgcolor=""> <th>DESCRIPTION</th> <td>Child Care Services</td> </tr><tr bgcolor="#E3E3F3"> <th>HYPERLINK</th> <td></td> </tr><tr bgcolor=""> <th>LANDXADDRESSPOINT</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>LANDYADDRESSPOINT</th> <td></td> </tr><tr bgcolor=""> <th>NAME</th> <td>PCF SPARKLETOTS PRESCHOOL @ TELOK BLANGAH BLK 44 (CC)</td> </tr><tr bgcolor="#E3E3F3"> <th>PHOTOURL</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSFLOORNUMBER</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>INC_CRC</th> <td>349C54F201805938</td> </tr><tr bgcolor=""> <th>FMEL_UPD_D</th> <td>20211201093837</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSUNITNUMBER</th> <td></td> </tr></table></center> 
max values  : kml_999,                                            <center><table><tr><th colspan='2' align='center'><em>Attributes</em></th></tr><tr bgcolor="#E3E3F3"> <th>ADDRESSBLOCKHOUSENUMBER</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSBUILDINGNAME</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSPOSTALCODE</th> <td>99982</td> </tr><tr bgcolor=""> <th>ADDRESSSTREETNAME</th> <td>35, ALLANBROOKE ROAD, SINGAPORE 099982</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSTYPE</th> <td></td> </tr><tr bgcolor=""> <th>DESCRIPTION</th> <td>Child Care Services</td> </tr><tr bgcolor="#E3E3F3"> <th>HYPERLINK</th> <td></td> </tr><tr bgcolor=""> <th>LANDXADDRESSPOINT</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>LANDYADDRESSPOINT</th> <td></td> </tr><tr bgcolor=""> <th>NAME</th> <td>ISLANDER PRE-SCHOOL PTE LTD</td> </tr><tr bgcolor="#E3E3F3"> <th>PHOTOURL</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSFLOORNUMBER</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>INC_CRC</th> <td>4F63ACF93EFABE7F</td> </tr><tr bgcolor=""> <th>FMEL_UPD_D</th> <td>20211201093837</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSUNITNUMBER</th> <td></td> </tr></table></center> 

mpsz

class       : SpatialPolygonsDataFrame 
features    : 323 
extent      : 2667.538, 56396.44, 15748.72, 50256.33  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
variables   : 15
names       : OBJECTID, SUBZONE_NO, SUBZONE_N, SUBZONE_C, CA_IND, PLN_AREA_N, PLN_AREA_C,       REGION_N, REGION_C,          INC_CRC, FMEL_UPD_D,     X_ADDR,     Y_ADDR,    SHAPE_Leng,    SHAPE_Area 
min values  :        1,          1, ADMIRALTY,    AMSZ01,      N, ANG MO KIO,         AM, CENTRAL REGION,       CR, 00F5E30B5C9B7AD8,      16409,  5092.8949,  19579.069, 871.554887798, 39437.9352703 
max values  :      323,         17,    YUNNAN,    YSSZ09,      Y,     YISHUN,         YS,    WEST REGION,       WR, FFCCF172717C2EAF,      16409, 50424.7923, 49552.7904, 68083.9364708,  69748298.792 

sg

class       : SpatialPolygons 
features    : 1 
extent      : 2667.538, 56396.44, 15748.72, 50256.33  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 

Notice that the geospatial data have been converted into their respective sp’s Spatial* classes now.

4.5.2 Converting the Spatial* class into generic sp format

spatstat requires the analytical data in ppp object form. There is no direct way to convert a Spatial* classes into ppp object. We need to convert the Spatial classes* into Spatial object first.

The codes chunk below converts the Spatial* classes into generic sp objects.

childcare_sp <- as(childcare, "SpatialPoints")
sg_sp <- as(sg, "SpatialPolygons")

Next, you should display the sp objects properties as shown below.

childcare_sp

class       : SpatialPoints 
features    : 1925 
extent      : 11810.03, 45404.24, 25596.33, 49300.88  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 

sg_sp

class       : SpatialPolygons 
features    : 1 
extent      : 2667.538, 56396.44, 15748.72, 50256.33  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 

Challenge: Do you know what are the differences between Spatial* classes and generic sp object?

4.5.3 Converting the generic sp format into spatstat’s ppp format

Now, we will use as.ppp() function of spatstat to convert the spatial data into spatstat’s ppp object format.

childcare_ppp <- as(childcare_sp, "ppp")
childcare_ppp

Planar point pattern: 1925 points
window: rectangle = [11810.03, 45404.24] x [25596.33, 49300.88] units

Now, let us plot childcare_ppp and examine the different.

plot(childcare_ppp)

You can take a quick look at the summary statistics of the newly created ppp object by using the code chunk below.

summary(childcare_ppp)

Planar point pattern:  1925 points
Average intensity 2.417323e-06 points per square unit

*Pattern contains duplicated points*

Coordinates are given to 3 decimal places
i.e. rounded to the nearest multiple of 0.001 units

Window: rectangle = [11810.03, 45404.24] x [25596.33, 49300.88] units
                    (33590 x 23700 units)
Window area = 796335000 square units

Notice the warning message about duplicates. In spatial point patterns analysis an issue of significant is the presence of duplicates. The statistical methodology used for spatial point patterns processes is based largely on the assumption that process are simple, that is, that the points cannot be coincident.

4.5.4 Handling duplicated points

We can check the duplication in a ppp object by using the code chunk below.

any(duplicated(childcare_ppp))

[1] TRUE

To count the number of co-indicence point, we will use the multiplicity() function as shown in the code chunk below.

multiplicity(childcare_ppp)

   1    2    3    4    5    6    7    8    9   10   11   12   13   14   15   16 
   1    2    1    1    1    1    2    1    1    1    1    1    1    3    1    1 
  17   18   19   20   21   22   23   24   25   26   27   28   29   30   31   32 
   1    3    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
  33   34   35   36   37   38   39   40   41   42   43   44   45   46   47   48 
   1    1    1    1    4    1    1    1    1    1    1    1    1    1    1    2 
  49   50   51   52   53   54   55   56   57   58   59   60   61   62   63   64 
   1    1    1    2    1    1    1    1    1    1    1    1    1    2    1    1 
  65   66   67   68   69   70   71   72   73   74   75   76   77   78   79   80 
   1    3    1    1    1    2    1   10    1    1    1    1    1    1    1    1 
  81   82   83   84   85   86   87   88   89   90   91   92   93   94   95   96 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
  97   98   99  100  101  102  103  104  105  106  107  108  109  110  111  112 
   1    1    1    1    1    1    1    2    1    1    3    1    1    1    2    1 
 113  114  115  116  117  118  119  120  121  122  123  124  125  126  127  128 
   1    2    2    2    1    1    1    1    1    1    1    1    2    1    1    1 
 129  130  131  132  133  134  135  136  137  138  139  140  141  142  143  144 
   1    1    1    1    1    3    1    1    1    1    1    1    1    1    1    1 
 145  146  147  148  149  150  151  152  153  154  155  156  157  158  159  160 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 161  162  163  164  165  166  167  168  169  170  171  172  173  174  175  176 
   1    1    2    2    2    1    1    1    1    1    2    1    4    1    1    2 
 177  178  179  180  181  182  183  184  185  186  187  188  189  190  191  192 
   1    1    1    1    1    1    1    1    2    1    1    1    1    1    1    1 
 193  194  195  196  197  198  199  200  201  202  203  204  205  206  207  208 
   3    1    1    1    1    1    3    1    1    1    1    1    1    1    1    1 
 209  210  211  212  213  214  215  216  217  218  219  220  221  222  223  224 
   1    1    1    1    1   10    1    1    3    1    1    1    1    1    1    1 
 225  226  227  228  229  230  231  232  233  234  235  236  237  238  239  240 
   1    1    1    2    1    1    1    1    1    1    1    1    1    1    1    1 
 241  242  243  244  245  246  247  248  249  250  251  252  253  254  255  256 
   1    1    2    6    1    2    1    1    2    1    1    1    1    1    1    1 
 257  258  259  260  261  262  263  264  265  266  267  268  269  270  271  272 
   3    2    3    2    1    2    1    1    2    4    1    6    6    1    1    1 
 273  274  275  276  277  278  279  280  281  282  283  284  285  286  287  288 
   2    1    1    1    1    2    1    1    1    1    1    1    3    1    1    1 
 289  290  291  292  293  294  295  296  297  298  299  300  301  302  303  304 
   1    1    4    1    2    1    1    1    1    1    1    1    1    1    1    1 
 305  306  307  308  309  310  311  312  313  314  315  316  317  318  319  320 
   1    1    1    1    1    1    1    1    1    1    1    2    1    1    1    1 
 321  322  323  324  325  326  327  328  329  330  331  332  333  334  335  336 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 337  338  339  340  341  342  343  344  345  346  347  348  349  350  351  352 
   1    1    2    1    1    1    2    1    1    1    2    1    1    1    1    1 
 353  354  355  356  357  358  359  360  361  362  363  364  365  366  367  368 
   1    1    1    1    2    1    2    2    1    1    1    1    2    1    1    1 
 369  370  371  372  373  374  375  376  377  378  379  380  381  382  383  384 
   4    1    1    1    1    2    1    1    1    1    1    1    2    1    1    1 
 385  386  387  388  389  390  391  392  393  394  395  396  397  398  399  400 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    2 
 401  402  403  404  405  406  407  408  409  410  411  412  413  414  415  416 
   2    1    1    1    1    1    1    1    1    1    1    1    1    1    1    4 
 417  418  419  420  421  422  423  424  425  426  427  428  429  430  431  432 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 433  434  435  436  437  438  439  440  441  442  443  444  445  446  447  448 
   1    1    1    1    1    1    1    1    1    2    1    1    1    1    1    1 
 449  450  451  452  453  454  455  456  457  458  459  460  461  462  463  464 
   1    1    2    1    1    1    1    1    1    1    1    1    2    1    1    1 
 465  466  467  468  469  470  471  472  473  474  475  476  477  478  479  480 
   1    1    2    1    1    1    1    1    1    1    1    1    1    1    1    1 
 481  482  483  484  485  486  487  488  489  490  491  492  493  494  495  496 
   2    2    1    1    1    1    1   10    1    2    1    1    1    2    1    3 
 497  498  499  500  501  502  503  504  505  506  507  508  509  510  511  512 
   1    1    1    1   10   10   10    1    1    1    1    1    1    1    1    1 
 513  514  515  516  517  518  519  520  521  522  523  524  525  526  527  528 
   1    1    1    2    1    2    1    1    1    1    3    1    2    1    1    1 
 529  530  531  532  533  534  535  536  537  538  539  540  541  542  543  544 
   1    1    1    1    1    1    3    1    1    1    1    1    2    1    1    2 
 545  546  547  548  549  550  551  552  553  554  555  556  557  558  559  560 
   1    1    3    1    1    1    1    1    1    1    1    2    2    2    1    1 
 561  562  563  564  565  566  567  568  569  570  571  572  573  574  575  576 
   2    3    1    1    1    2    1    1    1    2    2    1    1    1    1    1 
 577  578  579  580  581  582  583  584  585  586  587  588  589  590  591  592 
   1    1    1    1    1    1    1    1    1    1    1    1    1    4    1    1 
 593  594  595  596  597  598  599  600  601  602  603  604  605  606  607  608 
   1    1    1    1    1    3    1    1    1    1    1    1    1    1    1    1 
 609  610  611  612  613  614  615  616  617  618  619  620  621  622  623  624 
   1    1    1    1    1    4    1    1    1    1    1    1    4    1    1    1 
 625  626  627  628  629  630  631  632  633  634  635  636  637  638  639  640 
   1    1    1    1    1    2    1    1    1    1    1    1    1    1    1    1 
 641  642  643  644  645  646  647  648  649  650  651  652  653  654  655  656 
   1    1    1    1    2    1    1    1    1    1    1    1    1    2    1    1 
 657  658  659  660  661  662  663  664  665  666  667  668  669  670  671  672 
   1    1    1    1    1    1    1    1    1    1    2    1    1    3    1    1 
 673  674  675  676  677  678  679  680  681  682  683  684  685  686  687  688 
   1    1    1    1    1    1    1    1    1   10    1    1    1    1    1    2 
 689  690  691  692  693  694  695  696  697  698  699  700  701  702  703  704 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 705  706  707  708  709  710  711  712  713  714  715  716  717  718  719  720 
   1    1    1    2    1    2    1   10    1    4    1    2    1    1    1    1 
 721  722  723  724  725  726  727  728  729  730  731  732  733  734  735  736 
   3    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 737  738  739  740  741  742  743  744  745  746  747  748  749  750  751  752 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 753  754  755  756  757  758  759  760  761  762  763  764  765  766  767  768 
   1    3    1    1    3    1    1    1    1    2    1    1    1    1    1    1 
 769  770  771  772  773  774  775  776  777  778  779  780  781  782  783  784 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 785  786  787  788  789  790  791  792  793  794  795  796  797  798  799  800 
   1    1    1    1    1    1    1    1    1    1    2    1    1    1    1    1 
 801  802  803  804  805  806  807  808  809  810  811  812  813  814  815  816 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 817  818  819  820  821  822  823  824  825  826  827  828  829  830  831  832 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 833  834  835  836  837  838  839  840  841  842  843  844  845  846  847  848 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 849  850  851  852  853  854  855  856  857  858  859  860  861  862  863  864 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 865  866  867  868  869  870  871  872  873  874  875  876  877  878  879  880 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 881  882  883  884  885  886  887  888  889  890  891  892  893  894  895  896 
   1    1    1    1    1    1    1    1    1    2    1    1    1    1    1    2 
 897  898  899  900  901  902  903  904  905  906  907  908  909  910  911  912 
   1    1    1    2    1    1    1    1    1    1    1    1    1    1    1    1 
 913  914  915  916  917  918  919  920  921  922  923  924  925  926  927  928 
   1    1    2    1    1    1    1    1    2    2    1    1    1    1    2    1 
 929  930  931  932  933  934  935  936  937  938  939  940  941  942  943  944 
   1    1    2    1    2    1    1    1    2    1    1    1    2    1    1    1 
 945  946  947  948  949  950  951  952  953  954  955  956  957  958  959  960 
   1    1    2    1    1    2    1    1    1    1    1    1    1    1    2    1 
 961  962  963  964  965  966  967  968  969  970  971  972  973  974  975  976 
   1    2    2    1    1    1    1    2    1    1    1    1    2    1    1    2 
 977  978  979  980  981  982  983  984  985  986  987  988  989  990  991  992 
   1    1    1    1    2    1    1    1    1    1    1    1    1    1    1    1 
 993  994  995  996  997  998  999 1000 1001 1002 1003 1004 1005 1006 1007 1008 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 
   1    1    1    2    4    1    1    1    1    1    1    2    1    2    2    2 
1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 
   2    1    1    1    1    2    1    1    2    2    2    2    1    1    1    1 
1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 
   2    1    1    1    2    1    2    1    1    1    1    1    1    1    1    1 
1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 
   1    2    2    2    1    1    1    1    1    2    1    1    2    2    2    1 
1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 
   1    1    1    1    2    1    1    2    1    1    1    1    1    1    1    1 
1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 
   1    3    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 
   2    1    2    1    2    1    1    1    1    1    1    2    2    1    1    2 
1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 
   1    2    1    2    1    2    1    1    1    1    1    2    1    1    1    1 
1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 
   1    2    1    2    2    2    2    2    1    1    1    1    1    2    1    1 
1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 
   1    1    1    1    1    2    1    1    2    1    1    1    1    2    1    1 
1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 
   1    2    1    1    1    1    2    1    1    1    1    1    1    1    1    1 
1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 
   1    1    1    1    1    1    1    1    1    2    1    1    1    1    1    1 
1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 
   1    1    1    2    1    1    1    3    1    1    1    1    1    1    1   10 
1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 
   2    1    3    2    1    2    1    1    2    3    2    1    1    1    1    1 
1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 
   1    1    1    1    1    2    1    2    1    1    1    1    1    1    1    1 
1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 
   1    1    1    1    1    1    1    1    1    1    4    1    1    1    1    1 
1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 
   2    1    1    1    2    1    2    1    1    1    1    1    1    1    1    1 
1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 
  10    1    2    4    1    1    1    4    1    4    1    1    1    1    1    1 
1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 
   1    1    1    1    1    1    1    1    1    4    2    3    2    1    1    1 
1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 
   2    2    1    1    1    1    1    2    2    3    1    1    1    1    1    2 
1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 
   2    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 
   1    1    1    2    1    1    1    1    1    1    1    1    1    1    1    1 
1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 
   2    2    2    1    1    1    6    1    1    1    1    1    1    1    1    1 
1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 
   1    1    1    4    1    1    1    1    1    1    1    1    1    1    1    1 
1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 
   1    1    1    1    2    2    1    1    1    1    1    1    1    1    1    1 
1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 
   1    1    1    1    2    1    1    1    1    2    1    1    1    1    2    1 
1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 
   2    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 
   2    1    1    1    1    1    1    3    1    1    1    1    1    1    1    1 
1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 
   1    1    1    1    1    1    1    1    1    6    1    1    1    1    1    1 
1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 
   1    1    1    1    1    1    1    3    1    1    4    1    1    2    1    1 
1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 
   2    1    1    1    2    1    4    1    2    1    1    1    1    1    1    1 
1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 
   1    1    1    1    1    1    1    1    2    1    1    2    1    1    1    1 
1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 
   1    1    1    1    2    1    1    3    1    1    1    2    1    1    1    1 
1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 
   2    1    1    1    1    1    1    2    1    1    2    1    1    1    1    1 
1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 
   3    1    1    2    1    1    1    1    1    1    1    1    1    2    1    1 
1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 
   1    1    1    1    1    1    1    2    1    1    1    1    1    1    1    1 
1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 
   1    1    1    4    1    1    1    6    1    1    1    1    1    1    1    1 
1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 
   1    1    1    2    1    1    1    2    1    1    1    1    1    2    1    1 
1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 
   1    2    1    1    1    1    1    1    1    1    2    2    2    1    1    1 
1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 
   2    1    2    1    2    1    2    1    1    2    1    2    2    2    2    1 
1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 
   1    1    1    1    1    2    1    1    1    2    1    1    1    1    2    1 
1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 
   1    4    1    4    1    4    1    1    2    1    1    1    1    1    3    1 
1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 
   1    1    1    2    2    2    2    2    2    2    2    1    1    2    2    2 
1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 
   1    2    1    1    1    1    1    2    2    2    1    2    2    2    2    1 
1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 
   2    1    1    1    1    1    1    1    2    2    1    2    1    1    1    1 
1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 
   1    1    1    1    2    1    2    2    2    2    2    2    1    1    2    1 
1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 
   1    1    1    2    2    2    2    2    1    1    1    2    1    1    2    2 
1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 
   1    2    1    1    2    1    1    2    2    2    1    2    1    2    1    1 
1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 
   1    1    1    1    1    1    2    1    1    1    1    4    1    1    1    1 
1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 
   3    1    1    2    1    1    1    2    1    1    1    1    1    2    2    1 
1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 
   1    1    2    1    2    2    1    1    1    1    1    2    1    1    2    1 
1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 
   1    3    2    2    2    1    2    1    3    1    1    1    1    1    1    1 
1921 1922 1923 1924 1925 
   1    1    1    1    3 

If we want to know how many locations have more than one point event, we can use the code chunk below.

sum(multiplicity(childcare_ppp) > 1)

[1] 338

The output shows that there are 128 duplicated point events.

To view the locations of these duplicate point events, we will plot childcare data by using the code chunk below.

tmap_mode('view')

tmap mode set to interactive viewing

tm_shape(childcare) +
  tm_dots(alpha=0.4, 
          size=0.05)

tmap_mode('plot')

tmap mode set to plotting

Challenge: Do you know how to spot the duplicate points from the map shown above?

There are three ways to overcome this problem. The easiest way is to delete the duplicates. But, that will also mean that some useful point events will be lost.

The second solution is use jittering, which will add a small perturbation to the duplicate points so that they do not occupy the exact same space.

The third solution is to make each point “unique” and then attach the duplicates of the points to the patterns as marks, as attributes of the points. Then you would need analytical techniques that take into account these marks.

The code chunk below implements the jittering approach.

childcare_ppp_jit <- rjitter(childcare_ppp, 
                             retry=TRUE, 
                             nsim=1, 
                             drop=TRUE)

DIY: Using the method you learned in previous section, check if any dusplicated point in this geospatial data.

any(duplicated(childcare_ppp_jit))

[1] FALSE

4.5.5 Creating owin object

When analysing spatial point patterns, it is a good practice to confine the analysis with a geographical area like Singapore boundary. In spatstat, an object called owin is specially designed to represent this polygonal region.

The code chunk below is used to covert sg SpatialPolygon object into owin object of spatstat.

sg_owin <- as(sg_sp, "owin")

The ouput object can be displayed by using plot() function

plot(sg_owin)

and summary() function of Base R.

summary(sg_owin)

Window: polygonal boundary
80 separate polygons (35 holes)
                  vertices         area relative.area
polygon 1                4  9.47108e+01      1.21e-07
polygon 2               37  1.29481e+04      1.66e-05
polygon 3               30  4.28933e+03      5.49e-06
polygon 4              145  9.61782e+05      1.23e-03
polygon 5              227  1.10308e+06      1.41e-03
polygon 6               19  3.09221e+04      3.95e-05
polygon 7               10  6.60195e+03      8.44e-06
polygon 8              234  2.08755e+06      2.67e-03
polygon 9               22  6.74651e+03      8.63e-06
polygon 10              71  5.63061e+03      7.20e-06
polygon 11              10  1.99717e+02      2.55e-07
polygon 12           14663  6.97996e+08      8.93e-01
polygon 13 (hole)        3 -2.05920e-03     -2.63e-12
polygon 14 (hole)        3 -2.89050e-05     -3.70e-14
polygon 15 (hole)        3 -2.83151e-01     -3.62e-10
polygon 16 (hole)        3 -3.99521e-02     -5.11e-11
polygon 17 (hole)        3 -4.95057e-02     -6.33e-11
polygon 18 (hole)        3 -3.65501e-03     -4.67e-12
polygon 19 (hole)        4 -2.05611e-02     -2.63e-11
polygon 20 (hole)        3 -1.68316e-04     -2.15e-13
polygon 21 (hole)       26 -1.25665e+03     -1.61e-06
polygon 22 (hole)        3 -2.18000e-06     -2.79e-15
polygon 23 (hole)        3 -6.62377e-01     -8.47e-10
polygon 24 (hole)        3 -2.09065e-03     -2.67e-12
polygon 25 (hole)       36 -7.79904e+03     -9.97e-06
polygon 26 (hole)        3 -8.83647e-03     -1.13e-11
polygon 27 (hole)        3 -2.21090e+00     -2.83e-09
polygon 28 (hole)       40 -6.00381e+03     -7.68e-06
polygon 29 (hole)        7 -1.40545e-01     -1.80e-10
polygon 30 (hole)       20 -4.39069e+00     -5.62e-09
polygon 31 (hole)       28 -1.99862e+01     -2.56e-08
polygon 32 (hole)       48 -1.38338e+02     -1.77e-07
polygon 33 (hole)      351 -1.21433e+03     -1.55e-06
polygon 34 (hole)       12 -8.36709e+01     -1.07e-07
polygon 35 (hole)      317 -5.11280e+04     -6.54e-05
polygon 36 (hole)       36 -4.01660e+04     -5.14e-05
polygon 37              30  2.80002e+04      3.58e-05
polygon 38              27  1.50315e+04      1.92e-05
polygon 39              15  4.03300e+04      5.16e-05
polygon 40            1045  4.44510e+06      5.68e-03
polygon 41 (hole)       13 -3.91907e+02     -5.01e-07
polygon 42              47  3.82087e+04      4.89e-05
polygon 43              65  8.42861e+04      1.08e-04
polygon 44             478  2.06120e+06      2.64e-03
polygon 45             266  1.50631e+06      1.93e-03
polygon 46             234  4.72886e+05      6.05e-04
polygon 47              14  5.86546e+03      7.50e-06
polygon 48              83  5.28920e+03      6.76e-06
polygon 49              75  1.73526e+04      2.22e-05
polygon 50             148  3.10395e+03      3.97e-06
polygon 51             142  3.22293e+03      4.12e-06
polygon 52              45  2.51218e+03      3.21e-06
polygon 53              40  1.38607e+04      1.77e-05
polygon 54              10  4.90942e+02      6.28e-07
polygon 55              95  5.96187e+04      7.62e-05
polygon 56 (hole)        4 -1.86410e-02     -2.38e-11
polygon 57              64  3.43149e+04      4.39e-05
polygon 58 (hole)        3 -1.98390e-03     -2.54e-12
polygon 59 (hole)        3 -5.55856e-03     -7.11e-12
polygon 60 (hole)        3 -5.12482e-03     -6.55e-12
polygon 61 (hole)        3 -1.96410e-03     -2.51e-12
polygon 62 (hole)        4 -1.13774e-02     -1.46e-11
polygon 63             155  2.67502e+05      3.42e-04
polygon 64             106  3.04104e+03      3.89e-06
polygon 65            1027  1.27782e+06      1.63e-03
polygon 66 (hole)        3 -3.23310e-04     -4.13e-13
polygon 67 (hole)        3 -1.16959e-03     -1.50e-12
polygon 68 (hole)        3 -1.46474e-03     -1.87e-12
polygon 69             211  4.70521e+05      6.02e-04
polygon 70               4  2.69313e+02      3.44e-07
polygon 71             132  9.53357e+04      1.22e-04
polygon 72               6  4.50259e+02      5.76e-07
polygon 73             285  1.61128e+06      2.06e-03
polygon 74              91  1.49663e+04      1.91e-05
polygon 75              71  8.18750e+03      1.05e-05
polygon 76             668  5.40368e+07      6.91e-02
polygon 77              77  3.29939e+05      4.22e-04
polygon 78             711  1.28815e+07      1.65e-02
polygon 79 (hole)        3 -3.41405e-01     -4.37e-10
polygon 80              44  2.26577e+03      2.90e-06
enclosing rectangle: [2667.54, 56396.44] x [15748.72, 50256.33] units
                     (53730 x 34510 units)
Window area = 781945000 square units
Fraction of frame area: 0.422

4.5.6 Combining point events object and owin object

In this last step of geospatial data wrangling, we will extract childcare events that are located within Singapore by using the code chunk below.

childcareSG_ppp = childcare_ppp[sg_owin]

The output object combined both the point and polygon feature in one ppp object class as shown below.

summary(childcareSG_ppp)

Planar point pattern:  1925 points
Average intensity 2.461811e-06 points per square unit

*Pattern contains duplicated points*

Coordinates are given to 3 decimal places
i.e. rounded to the nearest multiple of 0.001 units

Window: polygonal boundary
80 separate polygons (35 holes)
                  vertices         area relative.area
polygon 1                4  9.47108e+01      1.21e-07
polygon 2               37  1.29481e+04      1.66e-05
polygon 3               30  4.28933e+03      5.49e-06
polygon 4              145  9.61782e+05      1.23e-03
polygon 5              227  1.10308e+06      1.41e-03
polygon 6               19  3.09221e+04      3.95e-05
polygon 7               10  6.60195e+03      8.44e-06
polygon 8              234  2.08755e+06      2.67e-03
polygon 9               22  6.74651e+03      8.63e-06
polygon 10              71  5.63061e+03      7.20e-06
polygon 11              10  1.99717e+02      2.55e-07
polygon 12           14663  6.97996e+08      8.93e-01
polygon 13 (hole)        3 -2.05920e-03     -2.63e-12
polygon 14 (hole)        3 -2.89050e-05     -3.70e-14
polygon 15 (hole)        3 -2.83151e-01     -3.62e-10
polygon 16 (hole)        3 -3.99521e-02     -5.11e-11
polygon 17 (hole)        3 -4.95057e-02     -6.33e-11
polygon 18 (hole)        3 -3.65501e-03     -4.67e-12
polygon 19 (hole)        4 -2.05611e-02     -2.63e-11
polygon 20 (hole)        3 -1.68316e-04     -2.15e-13
polygon 21 (hole)       26 -1.25665e+03     -1.61e-06
polygon 22 (hole)        3 -2.18000e-06     -2.79e-15
polygon 23 (hole)        3 -6.62377e-01     -8.47e-10
polygon 24 (hole)        3 -2.09065e-03     -2.67e-12
polygon 25 (hole)       36 -7.79904e+03     -9.97e-06
polygon 26 (hole)        3 -8.83647e-03     -1.13e-11
polygon 27 (hole)        3 -2.21090e+00     -2.83e-09
polygon 28 (hole)       40 -6.00381e+03     -7.68e-06
polygon 29 (hole)        7 -1.40545e-01     -1.80e-10
polygon 30 (hole)       20 -4.39069e+00     -5.62e-09
polygon 31 (hole)       28 -1.99862e+01     -2.56e-08
polygon 32 (hole)       48 -1.38338e+02     -1.77e-07
polygon 33 (hole)      351 -1.21433e+03     -1.55e-06
polygon 34 (hole)       12 -8.36709e+01     -1.07e-07
polygon 35 (hole)      317 -5.11280e+04     -6.54e-05
polygon 36 (hole)       36 -4.01660e+04     -5.14e-05
polygon 37              30  2.80002e+04      3.58e-05
polygon 38              27  1.50315e+04      1.92e-05
polygon 39              15  4.03300e+04      5.16e-05
polygon 40            1045  4.44510e+06      5.68e-03
polygon 41 (hole)       13 -3.91907e+02     -5.01e-07
polygon 42              47  3.82087e+04      4.89e-05
polygon 43              65  8.42861e+04      1.08e-04
polygon 44             478  2.06120e+06      2.64e-03
polygon 45             266  1.50631e+06      1.93e-03
polygon 46             234  4.72886e+05      6.05e-04
polygon 47              14  5.86546e+03      7.50e-06
polygon 48              83  5.28920e+03      6.76e-06
polygon 49              75  1.73526e+04      2.22e-05
polygon 50             148  3.10395e+03      3.97e-06
polygon 51             142  3.22293e+03      4.12e-06
polygon 52              45  2.51218e+03      3.21e-06
polygon 53              40  1.38607e+04      1.77e-05
polygon 54              10  4.90942e+02      6.28e-07
polygon 55              95  5.96187e+04      7.62e-05
polygon 56 (hole)        4 -1.86410e-02     -2.38e-11
polygon 57              64  3.43149e+04      4.39e-05
polygon 58 (hole)        3 -1.98390e-03     -2.54e-12
polygon 59 (hole)        3 -5.55856e-03     -7.11e-12
polygon 60 (hole)        3 -5.12482e-03     -6.55e-12
polygon 61 (hole)        3 -1.96410e-03     -2.51e-12
polygon 62 (hole)        4 -1.13774e-02     -1.46e-11
polygon 63             155  2.67502e+05      3.42e-04
polygon 64             106  3.04104e+03      3.89e-06
polygon 65            1027  1.27782e+06      1.63e-03
polygon 66 (hole)        3 -3.23310e-04     -4.13e-13
polygon 67 (hole)        3 -1.16959e-03     -1.50e-12
polygon 68 (hole)        3 -1.46474e-03     -1.87e-12
polygon 69             211  4.70521e+05      6.02e-04
polygon 70               4  2.69313e+02      3.44e-07
polygon 71             132  9.53357e+04      1.22e-04
polygon 72               6  4.50259e+02      5.76e-07
polygon 73             285  1.61128e+06      2.06e-03
polygon 74              91  1.49663e+04      1.91e-05
polygon 75              71  8.18750e+03      1.05e-05
polygon 76             668  5.40368e+07      6.91e-02
polygon 77              77  3.29939e+05      4.22e-04
polygon 78             711  1.28815e+07      1.65e-02
polygon 79 (hole)        3 -3.41405e-01     -4.37e-10
polygon 80              44  2.26577e+03      2.90e-06
enclosing rectangle: [2667.54, 56396.44] x [15748.72, 50256.33] units
                     (53730 x 34510 units)
Window area = 781945000 square units
Fraction of frame area: 0.422

DIY: Using the method you learned in previous exercise, plot the newly derived childcareSG_ppp as shown below.

plot(childcareSG_ppp)

4.6 First-order Spatial Point Patterns Analysis

In this section, you will learn how to perform first-order SPPA by using spatstat package. The hands-on exercise will focus on:

• deriving kernel density estimation (KDE) layer for visualising and exploring the intensity of point processes,

• performing Confirmatory Spatial Point Patterns Analysis by using Nearest Neighbour statistics.

4.6.1 Kernel Density Estimation

In this section, you will learn how to compute the kernel density estimation (KDE) of childcare services in Singapore.

4.6.1.1 Computing kernel density estimation using automatic bandwidth selection method

The code chunk below computes a kernel density by using the following configurations of density() of spatstat:

• bw.diggle() automatic bandwidth selection method. Other recommended methods are bw.CvL(), bw.scott() or bw.ppl().

• The smoothing kernel used is gaussian, which is the default. Other smoothing methods are: “epanechnikov”, “quartic” or “disc”.

• The intensity estimate is corrected for edge effect bias by using method described by Jones (1993) and Diggle (2010, equation 18.9). The default is FALSE.

kde_childcareSG_bw <- density(childcareSG_ppp,
                              sigma=bw.diggle,
                              edge=TRUE,
                            kernel="gaussian") 

The plot() function of Base R is then used to display the kernel density derived.

plot(kde_childcareSG_bw)

The density values of the output range from 0 to 0.000035 which is way too small to comprehend. This is because the default unit of measurement of svy21 is in meter. As a result, the density values computed is in “number of points per square meter”.

Before we move on to next section, it is good to know that you can retrieve the bandwidth used to compute the kde layer by using the code chunk below.

bw <- bw.diggle(childcareSG_ppp)
bw

   sigma 
295.4419 

4.6.1.2 Rescalling KDE values

In the code chunk below, rescale() is used to covert the unit of measurement from meter to kilometer.

childcareSG_ppp.km <- rescale(childcareSG_ppp, 1000, "km")

Now, we can re-run density() using the resale data set and plot the output kde map.

kde_childcareSG.bw <- density(childcareSG_ppp.km, sigma=bw.diggle, edge=TRUE, kernel="gaussian")
plot(kde_childcareSG.bw)

Notice that output image looks identical to the earlier version, the only changes in the data values (refer to the legend).

4.6.2 Working with different automatic badwidth methods

Beside bw.diggle(), there are three other spatstat functions can be used to determine the bandwidth, they are: bw.CvL(), bw.scott(), and bw.ppl().

Let us take a look at the bandwidth return by these automatic bandwidth calculation methods by using the code chunk below.

 bw.CvL(childcareSG_ppp.km)

  sigma 
4.54311 

bw.scott(childcareSG_ppp.km)

 sigma.x  sigma.y 
2.159749 1.396455 

bw.ppl(childcareSG_ppp.km)

    sigma 
0.3897017 

bw.diggle(childcareSG_ppp.km)

    sigma 
0.2954419 

Baddeley et. (2016) suggested the use of the bw.ppl() algorithm because in ther experience it tends to produce the more appropriate values when the pattern consists predominantly of tight clusters. But they also insist that if the purpose of once study is to detect a single tight cluster in the midst of random noise then the bw.diggle() method seems to work best.

The code chunk beow will be used to compare the output of using bw.diggle and bw.ppl methods.

kde_childcareSG.ppl <- density(childcareSG_ppp.km, 
                               sigma=bw.ppl, 
                               edge=TRUE,
                               kernel="gaussian")
par(mfrow=c(1,2))
plot(kde_childcareSG.bw, main = "bw.diggle")
plot(kde_childcareSG.ppl, main = "bw.ppl")

4.6.3 Working with different kernel methods

By default, the kernel method used in density.ppp() is gaussian. But there are three other options, namely: Epanechnikov, Quartic and Dics.

The code chunk below will be used to compute three more kernel density estimations by using these three kernel function.

par(mfrow=c(2,2))
plot(density(childcareSG_ppp.km, 
             sigma=bw.ppl, 
             edge=TRUE, 
             kernel="gaussian"), 
     main="Gaussian")
plot(density(childcareSG_ppp.km, 
             sigma=bw.ppl, 
             edge=TRUE, 
             kernel="epanechnikov"), 
     main="Epanechnikov")

Warning in density.ppp(childcareSG_ppp.km, sigma = bw.ppl, edge = TRUE, :
Bandwidth selection will be based on Gaussian kernel

plot(density(childcareSG_ppp.km, 
             sigma=bw.ppl, 
             edge=TRUE, 
             kernel="quartic"), 
     main="Quartic")

Warning in density.ppp(childcareSG_ppp.km, sigma = bw.ppl, edge = TRUE, :
Bandwidth selection will be based on Gaussian kernel

plot(density(childcareSG_ppp.km, 
             sigma=bw.ppl, 
             edge=TRUE, 
             kernel="disc"), 
     main="Disc")

Warning in density.ppp(childcareSG_ppp.km, sigma = bw.ppl, edge = TRUE, :
Bandwidth selection will be based on Gaussian kernel

4.7 Fixed and Adaptive KDE

4.7.1 Computing KDE by using fixed bandwidth

Next, you will compute a KDE layer by defining a bandwidth of 600 meter. Notice that in the code chunk below, the sigma value used is 0.6. This is because the unit of measurement of childcareSG_ppp.km object is in kilometer, hence the 600m is 0.6km.

kde_childcareSG_600 <- density(childcareSG_ppp.km, sigma=0.6, edge=TRUE, kernel="gaussian")
plot(kde_childcareSG_600)

4.7.2 Computing KDE by using adaptive bandwidth

Fixed bandwidth method is very sensitive to highly skew distribution of spatial point patterns over geographical units for example urban versus rural. One way to overcome this problem is by using adaptive bandwidth instead.

In this section, you will learn how to derive adaptive kernel density estimation by using density.adaptive() of spatstat.

kde_childcareSG_adaptive <- adaptive.density(childcareSG_ppp.km, method="kernel")
plot(kde_childcareSG_adaptive)

We can compare the fixed and adaptive kernel density estimation outputs by using the code chunk below.

par(mfrow=c(1,2))
plot(kde_childcareSG.bw, main = "Fixed bandwidth")
plot(kde_childcareSG_adaptive, main = "Adaptive bandwidth")

4.7.3 Converting KDE output into grid object.

The result is the same, we just convert it so that it is suitable for mapping purposes

gridded_kde_childcareSG_bw <- as.SpatialGridDataFrame.im(kde_childcareSG.bw)
spplot(gridded_kde_childcareSG_bw)

4.7.3.1 Converting gridded output into raster

Next, we will convert the gridded kernal density objects into RasterLayer object by using raster() of raster package.

kde_childcareSG_bw_raster <- raster(gridded_kde_childcareSG_bw)

Let us take a look at the properties of kde_childcareSG_bw_raster RasterLayer.

kde_childcareSG_bw_raster

class      : RasterLayer 
dimensions : 128, 128, 16384  (nrow, ncol, ncell)
resolution : 0.419757, 0.2695907  (x, y)
extent     : 2.667538, 56.39644, 15.74872, 50.25633  (xmin, xmax, ymin, ymax)
crs        : NA 
source     : memory
names      : v 
values     : -1.293897e-14, 37.27443  (min, max)

Notice that the crs property is NA.

4.7.3.2 Assigning projection systems

The code chunk below will be used to include the CRS information on kde_childcareSG_bw_raster RasterLayer.

projection(kde_childcareSG_bw_raster) <- CRS("+init=EPSG:3414")
kde_childcareSG_bw_raster

class      : RasterLayer 
dimensions : 128, 128, 16384  (nrow, ncol, ncell)
resolution : 0.419757, 0.2695907  (x, y)
extent     : 2.667538, 56.39644, 15.74872, 50.25633  (xmin, xmax, ymin, ymax)
crs        : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +units=m +no_defs 
source     : memory
names      : v 
values     : -1.293897e-14, 37.27443  (min, max)

Notice that the crs property is completed.

4.7.4 Visualising the output in tmap

Finally, we will display the raster in cartographic quality map using tmap package.

tm_shape(kde_childcareSG_bw_raster) + 
  tm_raster("v") +
  tm_layout(legend.position = c("right", "bottom"), frame = FALSE)

Variable(s) "v" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.

Notice that the raster values are encoded explicitly onto the raster pixel using the values in “v”” field.

4.7.5 Comparing Spatial Point Patterns using KDE

In this section, you will learn how to compare KDE of childcare at Ponggol, Tampines, Chua Chu Kang and Jurong West planning areas.

4.7.5.1 Extracting study area

The code chunk below will be used to extract the target planning areas.

pg = mpsz[mpsz@data$PLN_AREA_N == "PUNGGOL",]
tm = mpsz[mpsz@data$PLN_AREA_N == "TAMPINES",]
ck = mpsz[mpsz@data$PLN_AREA_N == "CHOA CHU KANG",]
jw = mpsz[mpsz@data$PLN_AREA_N == "JURONG WEST",]

Plotting target planning areas

par(mfrow=c(2,2))
plot(pg, main = "Ponggol")
plot(tm, main = "Tampines")
plot(ck, main = "Choa Chu Kang")
plot(jw, main = "Jurong West")

4.7.5.2 Converting the spatial point data frame into generic sp format

Next, we will convert these SpatialPolygonsDataFrame layers into generic spatialpolygons layers.

pg_sp = as(pg, "SpatialPolygons")
tm_sp = as(tm, "SpatialPolygons")
ck_sp = as(ck, "SpatialPolygons")
jw_sp = as(jw, "SpatialPolygons")

4.7.5.3 Creating owin object

Now, we will convert these SpatialPolygons objects into owin objects that is required by spatstat.

pg_owin = as(pg_sp, "owin")
tm_owin = as(tm_sp, "owin")
ck_owin = as(ck_sp, "owin")
jw_owin = as(jw_sp, "owin")

4.7.5.4 Combining childcare points and the study area

By using the code chunk below, we are able to extract childcare that is within the specific region to do our analysis later on.

childcare_pg_ppp = childcare_ppp_jit[pg_owin]
childcare_tm_ppp = childcare_ppp_jit[tm_owin]
childcare_ck_ppp = childcare_ppp_jit[ck_owin]
childcare_jw_ppp = childcare_ppp_jit[jw_owin]

Next, rescale() function is used to trasnform the unit of measurement from metre to kilometre.

childcare_pg_ppp.km = rescale(childcare_pg_ppp, 1000, "km")
childcare_tm_ppp.km = rescale(childcare_tm_ppp, 1000, "km")
childcare_ck_ppp.km = rescale(childcare_ck_ppp, 1000, "km")
childcare_jw_ppp.km = rescale(childcare_jw_ppp, 1000, "km")

The code chunk below is used to plot these four study areas and the locations of the childcare centres.

par(mfrow=c(2,2))
plot(childcare_pg_ppp.km, main="Punggol")
plot(childcare_tm_ppp.km, main="Tampines")
plot(childcare_ck_ppp.km, main="Choa Chu Kang")
plot(childcare_jw_ppp.km, main="Jurong West")

4.7.5.5 Computing KDE

The code chunk below will be used to compute the KDE of these four planning area. bw.diggle method is used to derive the bandwidth of each

par(mfrow=c(2,2))
plot(density(childcare_pg_ppp.km, 
             sigma=bw.diggle, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Punggol")
plot(density(childcare_tm_ppp.km, 
             sigma=bw.diggle, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Tempines")
plot(density(childcare_ck_ppp.km, 
             sigma=bw.diggle, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Choa Chu Kang")
plot(density(childcare_jw_ppp.km, 
             sigma=bw.diggle, 
             edge=TRUE, 
             kernel="gaussian"),
     main="JUrong West")

4.7.5.6 Computing fixed bandwidth KDE

For comparison purposes, we will use 250m as the bandwidth.

par(mfrow=c(2,2))
plot(density(childcare_ck_ppp.km, 
             sigma=0.25, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Chou Chu Kang")
plot(density(childcare_jw_ppp.km, 
             sigma=0.25, 
             edge=TRUE, 
             kernel="gaussian"),
     main="JUrong West")
plot(density(childcare_pg_ppp.km, 
             sigma=0.25, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Punggol")
plot(density(childcare_tm_ppp.km, 
             sigma=0.25, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Tampines")

4.8 Nearest Neighbour Analysis

In this section, we will perform the Clark-Evans test of aggregation for a spatial point pattern by using clarkevans.test() of statspat.

The test hypotheses are:

Ho = The distribution of childcare services are randomly distributed.

H1= The distribution of childcare services are not randomly distributed.

The 95% confident interval will be used.

4.8.1 Testing spatial point patterns using Clark and Evans Test

clarkevans.test(childcareSG_ppp,
                correction="none",
                clipregion="sg_owin",
                alternative=c("clustered"),
                nsim=99)

    Clark-Evans test
    No edge correction
    Z-test

data:  childcareSG_ppp
R = 0.49534, p-value < 2.2e-16
alternative hypothesis: clustered (R < 1)

What conclusion can you draw from the test result?

4.8.2 Clark and Evans Test: Choa Chu Kang planning area

In the code chunk below, clarkevans.test() of spatstat is used to performs Clark-Evans test of aggregation for childcare centre in Choa Chu Kang planning area.

clarkevans.test(childcare_ck_ppp,
                correction="none",
                clipregion=NULL,
                alternative=c("two.sided"),
                nsim=999)

    Clark-Evans test
    No edge correction
    Z-test

data:  childcare_ck_ppp
R = 0.86204, p-value = 0.02319
alternative hypothesis: two-sided

4.8.3 Clark and Evans Test: Tampines planning area

In the code chunk below, the similar test is used to analyse the spatial point patterns of childcare centre in Tampines planning area.

clarkevans.test(childcare_tm_ppp,
                correction="none",
                clipregion=NULL,
                alternative=c("two.sided"),
                nsim=999)

    Clark-Evans test
    No edge correction
    Z-test

data:  childcare_tm_ppp
R = 0.68869, p-value = 1.18e-10
alternative hypothesis: two-sided

5  2nd Order Spatial Point Patterns Analysis Methods

5.1 Overview

Spatial Point Pattern Analysis is the evaluation of the pattern or distribution, of a set of points on a surface. The point can be location of:

• events such as crime, traffic accident and disease onset, or

• business services (coffee and fastfood outlets) or facilities such as childcare and eldercare.

Using appropriate functions of spatstat, this hands-on exercise aims to discover the spatial point processes of childecare centres in Singapore.

The specific questions we would like to answer are as follows:

• are the childcare centres in Singapore randomly distributed throughout the country?

• if the answer is not, then the next logical question is where are the locations with higher concentration of childcare centres?

5.2 The data

To provide answers to the questions above, three data sets will be used. They are:

• CHILDCARE, a point feature data providing both location and attribute information of childcare centres. It was downloaded from Data.gov.sg and is in geojson format.

• MP14_SUBZONE_WEB_PL, a polygon feature data providing information of URA 2014 Master Plan Planning Subzone boundary data. It is in ESRI shapefile format. This data set was also downloaded from Data.gov.sg.

• CostalOutline, a polygon feature data showing the national boundary of Singapore. It is provided by SLA and is in ESRI shapefile format.

5.3 Installing and Loading the R packages

In this hands-on exercise, five R packages will be used, they are:

• sf, a relatively new R package specially designed to import, manage and process vector-based geospatial data in R.

• spatstat, which has a wide range of useful functions for point pattern analysis. In this hands-on exercise, it will be used to perform 1st- and 2nd-order spatial point patterns analysis and derive kernel density estimation (KDE) layer.

• raster which reads, writes, manipulates, analyses and model of gridded spatial data (i.e. raster). In this hands-on exercise, it will be used to convert image output generate by spatstat into raster format.

• maptools which provides a set of tools for manipulating geographic data. In this hands-on exercise, we mainly use it to convert Spatial objects into ppp format of spatstat.

• tmap which provides functions for plotting cartographic quality static point patterns maps or interactive maps by using leaflet API.

Use the code chunk below to install and launch the five R packages.

pacman::p_load(maptools, sf, raster, spatstat, tmap)

5.4 Spatial Data Wrangling

5.4.1 Importing the spatial data

In this section, st_read() of sf package will be used to import these three geospatial data sets into R.

childcare_sf = st_read("data/geospatial/ChildCareServices.geojson") %>%
  st_transform(crs = 3414)

Reading layer `ChildCareServices' from data source 
  `C:\AloysiusCedric\IS415-GAA\Hands-on_Ex\Hands-on_Ex03\data\geospatial\ChildCareServices.geojson' 
  using driver `GeoJSON'
Simple feature collection with 1925 features and 2 fields
Geometry type: POINT
Dimension:     XYZ
Bounding box:  xmin: 103.6878 ymin: 1.247759 xmax: 103.9897 ymax: 1.462134
z_range:       zmin: 0 zmax: 0
Geodetic CRS:  WGS 84

mpsz_sf = st_read(dsn="data/geospatial", layer="MP14_SUBZONE_WEB_PL")%>%
  st_transform(crs=3414)

Reading layer `MP14_SUBZONE_WEB_PL' from data source 
  `C:\AloysiusCedric\IS415-GAA\Hands-on_Ex\Hands-on_Ex03\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21

st_crs(mpsz_sf)

Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]

sg_sf = st_union(mpsz_sf)%>%
  st_transform(crs=3414)

#plot(sg_sf)

#sg_sf = st_transform(sg_sf, crs=3414)
plot(sg_sf)

sg_sf

Geometry set for 1 feature 
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21 / Singapore TM

MULTIPOLYGON (((17763.39 15889.1, 17758.6 15868...

st_crs(sg_sf)

Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]

Before we can use these data for analysis, it is important for us to ensure that they are projected in same projection system.

DIY: Using the appropriate sf function you learned in Hands-on Exercise 2, retrieve the referencing system information of these geospatial data.

Notice that except childcare_sf, both mpsz_sf and sg_sf do not have proper crs information.

DIY: Using the method you learned in Lesson 2, assign the correct crs to mpsz_sf and sg_sf simple feature data frames.

DIY: If necessary, changing the referencing system to Singapore national projected coordinate system.

5.4.2 Mapping the geospatial data sets

After checking the referencing system of each geospatial data data frame, it is also useful for us to plot a map to show their spatial patterns.

DIY: Using the mapping methods you learned in Hands-on Exercise 3, prepare a map as shown below.

tmap_mode('view')

tmap mode set to interactive viewing

tm_shape(childcare_sf)+
  tm_dots()

Notice that all the geospatial layers are within the same map extend. This shows that their referencing system and coordinate values are referred to similar spatial context. This is very important in any geospatial analysis.

Alternatively, we can also prepare a pin map by using the code chunk below.

tmap_mode('view')

tmap mode set to interactive viewing

tmap mode set to interactive viewing

tm_shape(childcare_sf)+
  tm_dots()

tmap_mode('plot')

tmap mode set to plotting

tmap mode set to plotting

Notice that at the interactive mode, tmap is using leaflet for R API. The advantage of this interactive pin map is it allows us to navigate and zoom around the map freely. We can also query the information of each simple feature (i.e. the point) by clicking of them. Last but not least, you can also change the background of the internet map layer. Currently, three internet map layers are provided. They are: ESRI.WorldGrayCanvas, OpenStreetMap, and ESRI.WorldTopoMap. The default is ESRI.WorldGrayCanvas.

Reminder: Always remember to switch back to plot mode after the interactive map. This is because, each interactive mode will consume a connection. You should also avoid displaying ecessive numbers of interactive maps (i.e. not more than 10) in one RMarkdown document when publish on Netlify.

5.5 Geospatial Data wrangling

Although simple feature data frame is gaining popularity again sp’s Spatial* classes, there are, however, many geospatial analysis packages require the input geospatial data in sp’s Spatial* classes. In this section, you will learn how to convert simple feature data frame to sp’s Spatial* class.

5.5.1 Converting sf data frames to sp’s Spatial* class

The code chunk below uses as_Spatial() of sf package to convert the three geospatial data from simple feature data frame to sp’s Spatial* class.

childcare <- as_Spatial(childcare_sf)
mpsz <- as_Spatial(mpsz_sf)
sg <- as_Spatial(sg_sf)

childcare

class       : SpatialPointsDataFrame 
features    : 1925 
extent      : 11810.03, 45404.24, 25596.33, 49300.88  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
variables   : 2
names       :    Name,                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Description 
min values  :   kml_1, <center><table><tr><th colspan='2' align='center'><em>Attributes</em></th></tr><tr bgcolor="#E3E3F3"> <th>ADDRESSBLOCKHOUSENUMBER</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSBUILDINGNAME</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSPOSTALCODE</th> <td>100044</td> </tr><tr bgcolor=""> <th>ADDRESSSTREETNAME</th> <td>44, TELOK BLANGAH DRIVE, #01 - 19/51, SINGAPORE 100044</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSTYPE</th> <td></td> </tr><tr bgcolor=""> <th>DESCRIPTION</th> <td>Child Care Services</td> </tr><tr bgcolor="#E3E3F3"> <th>HYPERLINK</th> <td></td> </tr><tr bgcolor=""> <th>LANDXADDRESSPOINT</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>LANDYADDRESSPOINT</th> <td></td> </tr><tr bgcolor=""> <th>NAME</th> <td>PCF SPARKLETOTS PRESCHOOL @ TELOK BLANGAH BLK 44 (CC)</td> </tr><tr bgcolor="#E3E3F3"> <th>PHOTOURL</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSFLOORNUMBER</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>INC_CRC</th> <td>349C54F201805938</td> </tr><tr bgcolor=""> <th>FMEL_UPD_D</th> <td>20211201093837</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSUNITNUMBER</th> <td></td> </tr></table></center> 
max values  : kml_999,                                            <center><table><tr><th colspan='2' align='center'><em>Attributes</em></th></tr><tr bgcolor="#E3E3F3"> <th>ADDRESSBLOCKHOUSENUMBER</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSBUILDINGNAME</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSPOSTALCODE</th> <td>99982</td> </tr><tr bgcolor=""> <th>ADDRESSSTREETNAME</th> <td>35, ALLANBROOKE ROAD, SINGAPORE 099982</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSTYPE</th> <td></td> </tr><tr bgcolor=""> <th>DESCRIPTION</th> <td>Child Care Services</td> </tr><tr bgcolor="#E3E3F3"> <th>HYPERLINK</th> <td></td> </tr><tr bgcolor=""> <th>LANDXADDRESSPOINT</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>LANDYADDRESSPOINT</th> <td></td> </tr><tr bgcolor=""> <th>NAME</th> <td>ISLANDER PRE-SCHOOL PTE LTD</td> </tr><tr bgcolor="#E3E3F3"> <th>PHOTOURL</th> <td></td> </tr><tr bgcolor=""> <th>ADDRESSFLOORNUMBER</th> <td></td> </tr><tr bgcolor="#E3E3F3"> <th>INC_CRC</th> <td>4F63ACF93EFABE7F</td> </tr><tr bgcolor=""> <th>FMEL_UPD_D</th> <td>20211201093837</td> </tr><tr bgcolor="#E3E3F3"> <th>ADDRESSUNITNUMBER</th> <td></td> </tr></table></center> 

mpsz

class       : SpatialPolygonsDataFrame 
features    : 323 
extent      : 2667.538, 56396.44, 15748.72, 50256.33  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 
variables   : 15
names       : OBJECTID, SUBZONE_NO, SUBZONE_N, SUBZONE_C, CA_IND, PLN_AREA_N, PLN_AREA_C,       REGION_N, REGION_C,          INC_CRC, FMEL_UPD_D,     X_ADDR,     Y_ADDR,    SHAPE_Leng,    SHAPE_Area 
min values  :        1,          1, ADMIRALTY,    AMSZ01,      N, ANG MO KIO,         AM, CENTRAL REGION,       CR, 00F5E30B5C9B7AD8,      16409,  5092.8949,  19579.069, 871.554887798, 39437.9352703 
max values  :      323,         17,    YUNNAN,    YSSZ09,      Y,     YISHUN,         YS,    WEST REGION,       WR, FFCCF172717C2EAF,      16409, 50424.7923, 49552.7904, 68083.9364708,  69748298.792 

sg

class       : SpatialPolygons 
features    : 1 
extent      : 2667.538, 56396.44, 15748.72, 50256.33  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 

5.5.2 Converting the Spatial* class into generic sp format

spatstat requires the analytical data in ppp object form. There is no direct way to convert a Spatial* classes into ppp object. We need to convert the Spatial classes* into Spatial object first.

The codes chunk below converts the Spatial* classes into generic sp objects.

childcare_sp <- as(childcare, "SpatialPoints")
sg_sp <- as(sg, "SpatialPolygons")

Next, you should display the sp objects properties as shown below.

childcare_sp

class       : SpatialPoints 
features    : 1925 
extent      : 11810.03, 45404.24, 25596.33, 49300.88  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 

sg_sp

class       : SpatialPolygons 
features    : 1 
extent      : 2667.538, 56396.44, 15748.72, 50256.33  (xmin, xmax, ymin, ymax)
crs         : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs 

Challenge: Do you know what are the differences between Spatial* classes and generic sp object?

5.5.3 Converting the generic sp format into spatstat’s ppp format

Now, we will use as.ppp() function of spatstat to convert the spatial data into spatstat’s ppp object format.

childcare_ppp <- as(childcare_sp, "ppp")
childcare_ppp

Planar point pattern: 1925 points
window: rectangle = [11810.03, 45404.24] x [25596.33, 49300.88] units

Now, let us plot childcare_ppp and examine the different.

plot(childcare_ppp)

You can take a quick look at the summary statistics of the newly created ppp object by using the code chunk below.

summary(childcare_ppp)

Planar point pattern:  1925 points
Average intensity 2.417323e-06 points per square unit

*Pattern contains duplicated points*

Coordinates are given to 3 decimal places
i.e. rounded to the nearest multiple of 0.001 units

Window: rectangle = [11810.03, 45404.24] x [25596.33, 49300.88] units
                    (33590 x 23700 units)
Window area = 796335000 square units

Notice the warning message about duplicates. In spatial point patterns analysis an issue of significant is the presence of duplicates. The statistical methodology used for spatial point patterns processes is based largely on the assumption that process are simple, that is, that the points cannot be coincident.

5.5.4 Handling duplicated points

We can check the duplication in a ppp object by using the code chunk below.

any(duplicated(childcare_ppp))

[1] TRUE

To count the number of co-indicence point, we will use the multiplicity() function as shown in the code chunk below.

multiplicity(childcare_ppp)

   1    2    3    4    5    6    7    8    9   10   11   12   13   14   15   16 
   1    2    1    1    1    1    2    1    1    1    1    1    1    3    1    1 
  17   18   19   20   21   22   23   24   25   26   27   28   29   30   31   32 
   1    3    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
  33   34   35   36   37   38   39   40   41   42   43   44   45   46   47   48 
   1    1    1    1    4    1    1    1    1    1    1    1    1    1    1    2 
  49   50   51   52   53   54   55   56   57   58   59   60   61   62   63   64 
   1    1    1    2    1    1    1    1    1    1    1    1    1    2    1    1 
  65   66   67   68   69   70   71   72   73   74   75   76   77   78   79   80 
   1    3    1    1    1    2    1   10    1    1    1    1    1    1    1    1 
  81   82   83   84   85   86   87   88   89   90   91   92   93   94   95   96 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
  97   98   99  100  101  102  103  104  105  106  107  108  109  110  111  112 
   1    1    1    1    1    1    1    2    1    1    3    1    1    1    2    1 
 113  114  115  116  117  118  119  120  121  122  123  124  125  126  127  128 
   1    2    2    2    1    1    1    1    1    1    1    1    2    1    1    1 
 129  130  131  132  133  134  135  136  137  138  139  140  141  142  143  144 
   1    1    1    1    1    3    1    1    1    1    1    1    1    1    1    1 
 145  146  147  148  149  150  151  152  153  154  155  156  157  158  159  160 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 161  162  163  164  165  166  167  168  169  170  171  172  173  174  175  176 
   1    1    2    2    2    1    1    1    1    1    2    1    4    1    1    2 
 177  178  179  180  181  182  183  184  185  186  187  188  189  190  191  192 
   1    1    1    1    1    1    1    1    2    1    1    1    1    1    1    1 
 193  194  195  196  197  198  199  200  201  202  203  204  205  206  207  208 
   3    1    1    1    1    1    3    1    1    1    1    1    1    1    1    1 
 209  210  211  212  213  214  215  216  217  218  219  220  221  222  223  224 
   1    1    1    1    1   10    1    1    3    1    1    1    1    1    1    1 
 225  226  227  228  229  230  231  232  233  234  235  236  237  238  239  240 
   1    1    1    2    1    1    1    1    1    1    1    1    1    1    1    1 
 241  242  243  244  245  246  247  248  249  250  251  252  253  254  255  256 
   1    1    2    6    1    2    1    1    2    1    1    1    1    1    1    1 
 257  258  259  260  261  262  263  264  265  266  267  268  269  270  271  272 
   3    2    3    2    1    2    1    1    2    4    1    6    6    1    1    1 
 273  274  275  276  277  278  279  280  281  282  283  284  285  286  287  288 
   2    1    1    1    1    2    1    1    1    1    1    1    3    1    1    1 
 289  290  291  292  293  294  295  296  297  298  299  300  301  302  303  304 
   1    1    4    1    2    1    1    1    1    1    1    1    1    1    1    1 
 305  306  307  308  309  310  311  312  313  314  315  316  317  318  319  320 
   1    1    1    1    1    1    1    1    1    1    1    2    1    1    1    1 
 321  322  323  324  325  326  327  328  329  330  331  332  333  334  335  336 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 337  338  339  340  341  342  343  344  345  346  347  348  349  350  351  352 
   1    1    2    1    1    1    2    1    1    1    2    1    1    1    1    1 
 353  354  355  356  357  358  359  360  361  362  363  364  365  366  367  368 
   1    1    1    1    2    1    2    2    1    1    1    1    2    1    1    1 
 369  370  371  372  373  374  375  376  377  378  379  380  381  382  383  384 
   4    1    1    1    1    2    1    1    1    1    1    1    2    1    1    1 
 385  386  387  388  389  390  391  392  393  394  395  396  397  398  399  400 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    2 
 401  402  403  404  405  406  407  408  409  410  411  412  413  414  415  416 
   2    1    1    1    1    1    1    1    1    1    1    1    1    1    1    4 
 417  418  419  420  421  422  423  424  425  426  427  428  429  430  431  432 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 433  434  435  436  437  438  439  440  441  442  443  444  445  446  447  448 
   1    1    1    1    1    1    1    1    1    2    1    1    1    1    1    1 
 449  450  451  452  453  454  455  456  457  458  459  460  461  462  463  464 
   1    1    2    1    1    1    1    1    1    1    1    1    2    1    1    1 
 465  466  467  468  469  470  471  472  473  474  475  476  477  478  479  480 
   1    1    2    1    1    1    1    1    1    1    1    1    1    1    1    1 
 481  482  483  484  485  486  487  488  489  490  491  492  493  494  495  496 
   2    2    1    1    1    1    1   10    1    2    1    1    1    2    1    3 
 497  498  499  500  501  502  503  504  505  506  507  508  509  510  511  512 
   1    1    1    1   10   10   10    1    1    1    1    1    1    1    1    1 
 513  514  515  516  517  518  519  520  521  522  523  524  525  526  527  528 
   1    1    1    2    1    2    1    1    1    1    3    1    2    1    1    1 
 529  530  531  532  533  534  535  536  537  538  539  540  541  542  543  544 
   1    1    1    1    1    1    3    1    1    1    1    1    2    1    1    2 
 545  546  547  548  549  550  551  552  553  554  555  556  557  558  559  560 
   1    1    3    1    1    1    1    1    1    1    1    2    2    2    1    1 
 561  562  563  564  565  566  567  568  569  570  571  572  573  574  575  576 
   2    3    1    1    1    2    1    1    1    2    2    1    1    1    1    1 
 577  578  579  580  581  582  583  584  585  586  587  588  589  590  591  592 
   1    1    1    1    1    1    1    1    1    1    1    1    1    4    1    1 
 593  594  595  596  597  598  599  600  601  602  603  604  605  606  607  608 
   1    1    1    1    1    3    1    1    1    1    1    1    1    1    1    1 
 609  610  611  612  613  614  615  616  617  618  619  620  621  622  623  624 
   1    1    1    1    1    4    1    1    1    1    1    1    4    1    1    1 
 625  626  627  628  629  630  631  632  633  634  635  636  637  638  639  640 
   1    1    1    1    1    2    1    1    1    1    1    1    1    1    1    1 
 641  642  643  644  645  646  647  648  649  650  651  652  653  654  655  656 
   1    1    1    1    2    1    1    1    1    1    1    1    1    2    1    1 
 657  658  659  660  661  662  663  664  665  666  667  668  669  670  671  672 
   1    1    1    1    1    1    1    1    1    1    2    1    1    3    1    1 
 673  674  675  676  677  678  679  680  681  682  683  684  685  686  687  688 
   1    1    1    1    1    1    1    1    1   10    1    1    1    1    1    2 
 689  690  691  692  693  694  695  696  697  698  699  700  701  702  703  704 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 705  706  707  708  709  710  711  712  713  714  715  716  717  718  719  720 
   1    1    1    2    1    2    1   10    1    4    1    2    1    1    1    1 
 721  722  723  724  725  726  727  728  729  730  731  732  733  734  735  736 
   3    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 737  738  739  740  741  742  743  744  745  746  747  748  749  750  751  752 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 753  754  755  756  757  758  759  760  761  762  763  764  765  766  767  768 
   1    3    1    1    3    1    1    1    1    2    1    1    1    1    1    1 
 769  770  771  772  773  774  775  776  777  778  779  780  781  782  783  784 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 785  786  787  788  789  790  791  792  793  794  795  796  797  798  799  800 
   1    1    1    1    1    1    1    1    1    1    2    1    1    1    1    1 
 801  802  803  804  805  806  807  808  809  810  811  812  813  814  815  816 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 817  818  819  820  821  822  823  824  825  826  827  828  829  830  831  832 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 833  834  835  836  837  838  839  840  841  842  843  844  845  846  847  848 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 849  850  851  852  853  854  855  856  857  858  859  860  861  862  863  864 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 865  866  867  868  869  870  871  872  873  874  875  876  877  878  879  880 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
 881  882  883  884  885  886  887  888  889  890  891  892  893  894  895  896 
   1    1    1    1    1    1    1    1    1    2    1    1    1    1    1    2 
 897  898  899  900  901  902  903  904  905  906  907  908  909  910  911  912 
   1    1    1    2    1    1    1    1    1    1    1    1    1    1    1    1 
 913  914  915  916  917  918  919  920  921  922  923  924  925  926  927  928 
   1    1    2    1    1    1    1    1    2    2    1    1    1    1    2    1 
 929  930  931  932  933  934  935  936  937  938  939  940  941  942  943  944 
   1    1    2    1    2    1    1    1    2    1    1    1    2    1    1    1 
 945  946  947  948  949  950  951  952  953  954  955  956  957  958  959  960 
   1    1    2    1    1    2    1    1    1    1    1    1    1    1    2    1 
 961  962  963  964  965  966  967  968  969  970  971  972  973  974  975  976 
   1    2    2    1    1    1    1    2    1    1    1    1    2    1    1    2 
 977  978  979  980  981  982  983  984  985  986  987  988  989  990  991  992 
   1    1    1    1    2    1    1    1    1    1    1    1    1    1    1    1 
 993  994  995  996  997  998  999 1000 1001 1002 1003 1004 1005 1006 1007 1008 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 
   1    1    1    2    4    1    1    1    1    1    1    2    1    2    2    2 
1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 
   2    1    1    1    1    2    1    1    2    2    2    2    1    1    1    1 
1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 
   2    1    1    1    2    1    2    1    1    1    1    1    1    1    1    1 
1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 
   1    2    2    2    1    1    1    1    1    2    1    1    2    2    2    1 
1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 
   1    1    1    1    2    1    1    2    1    1    1    1    1    1    1    1 
1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 
   1    3    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 
   2    1    2    1    2    1    1    1    1    1    1    2    2    1    1    2 
1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 
   1    2    1    2    1    2    1    1    1    1    1    2    1    1    1    1 
1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 
   1    2    1    2    2    2    2    2    1    1    1    1    1    2    1    1 
1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 
   1    1    1    1    1    2    1    1    2    1    1    1    1    2    1    1 
1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 
   1    2    1    1    1    1    2    1    1    1    1    1    1    1    1    1 
1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 
   1    1    1    1    1    1    1    1    1    2    1    1    1    1    1    1 
1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 
   1    1    1    2    1    1    1    3    1    1    1    1    1    1    1   10 
1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 
   2    1    3    2    1    2    1    1    2    3    2    1    1    1    1    1 
1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 
   1    1    1    1    1    2    1    2    1    1    1    1    1    1    1    1 
1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 
   1    1    1    1    1    1    1    1    1    1    4    1    1    1    1    1 
1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 
   2    1    1    1    2    1    2    1    1    1    1    1    1    1    1    1 
1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 
  10    1    2    4    1    1    1    4    1    4    1    1    1    1    1    1 
1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 
   1    1    1    1    1    1    1    1    1    4    2    3    2    1    1    1 
1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 
   2    2    1    1    1    1    1    2    2    3    1    1    1    1    1    2 
1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 
   2    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 
   1    1    1    2    1    1    1    1    1    1    1    1    1    1    1    1 
1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 
   2    2    2    1    1    1    6    1    1    1    1    1    1    1    1    1 
1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 
   1    1    1    4    1    1    1    1    1    1    1    1    1    1    1    1 
1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 
   1    1    1    1    2    2    1    1    1    1    1    1    1    1    1    1 
1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 
   1    1    1    1    2    1    1    1    1    2    1    1    1    1    2    1 
1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 
   2    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 
   2    1    1    1    1    1    1    3    1    1    1    1    1    1    1    1 
1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 
   1    1    1    1    1    1    1    1    1    1    1    1    1    1    1    1 
1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 
   1    1    1    1    1    1    1    1    1    6    1    1    1    1    1    1 
1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 
   1    1    1    1    1    1    1    3    1    1    4    1    1    2    1    1 
1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 
   2    1    1    1    2    1    4    1    2    1    1    1    1    1    1    1 
1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 
   1    1    1    1    1    1    1    1    2    1    1    2    1    1    1    1 
1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 
   1    1    1    1    2    1    1    3    1    1    1    2    1    1    1    1 
1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 
   2    1    1    1    1    1    1    2    1    1    2    1    1    1    1    1 
1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 
   3    1    1    2    1    1    1    1    1    1    1    1    1    2    1    1 
1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 
   1    1    1    1    1    1    1    2    1    1    1    1    1    1    1    1 
1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 
   1    1    1    4    1    1    1    6    1    1    1    1    1    1    1    1 
1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 
   1    1    1    2    1    1    1    2    1    1    1    1    1    2    1    1 
1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 1708 1709 1710 1711 1712 
   1    2    1    1    1    1    1    1    1    1    2    2    2    1    1    1 
1713 1714 1715 1716 1717 1718 1719 1720 1721 1722 1723 1724 1725 1726 1727 1728 
   2    1    2    1    2    1    2    1    1    2    1    2    2    2    2    1 
1729 1730 1731 1732 1733 1734 1735 1736 1737 1738 1739 1740 1741 1742 1743 1744 
   1    1    1    1    1    2    1    1    1    2    1    1    1    1    2    1 
1745 1746 1747 1748 1749 1750 1751 1752 1753 1754 1755 1756 1757 1758 1759 1760 
   1    4    1    4    1    4    1    1    2    1    1    1    1    1    3    1 
1761 1762 1763 1764 1765 1766 1767 1768 1769 1770 1771 1772 1773 1774 1775 1776 
   1    1    1    2    2    2    2    2    2    2    2    1    1    2    2    2 
1777 1778 1779 1780 1781 1782 1783 1784 1785 1786 1787 1788 1789 1790 1791 1792 
   1    2    1    1    1    1    1    2    2    2    1    2    2    2    2    1 
1793 1794 1795 1796 1797 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 
   2    1    1    1    1    1    1    1    2    2    1    2    1    1    1    1 
1809 1810 1811 1812 1813 1814 1815 1816 1817 1818 1819 1820 1821 1822 1823 1824 
   1    1    1    1    2    1    2    2    2    2    2    2    1    1    2    1 
1825 1826 1827 1828 1829 1830 1831 1832 1833 1834 1835 1836 1837 1838 1839 1840 
   1    1    1    2    2    2    2    2    1    1    1    2    1    1    2    2 
1841 1842 1843 1844 1845 1846 1847 1848 1849 1850 1851 1852 1853 1854 1855 1856 
   1    2    1    1    2    1    1    2    2    2    1    2    1    2    1    1 
1857 1858 1859 1860 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 
   1    1    1    1    1    1    2    1    1    1    1    4    1    1    1    1 
1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 
   3    1    1    2    1    1    1    2    1    1    1    1    1    2    2    1 
1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 
   1    1    2    1    2    2    1    1    1    1    1    2    1    1    2    1 
1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 
   1    3    2    2    2    1    2    1    3    1    1    1    1    1    1    1 
1921 1922 1923 1924 1925 
   1    1    1    1    3 

If we want to know how many locations have more than one point event, we can use the code chunk below.

sum(multiplicity(childcare_ppp) > 1)

[1] 338

The output shows that there are 128 duplicated point events.

To view the locations of these duplicate point events, we will plot childcare data by using the code chunk below.

tmap_mode('view')

tmap mode set to interactive viewing

tmap mode set to interactive viewing

tm_shape(childcare) +
  tm_dots(alpha=0.4, 
          size=0.05)

tmap_mode('plot')

tmap mode set to plotting

tmap mode set to plotting

Challenge: Do you know how to spot the duplicate points from the map shown above?

There are three ways to overcome this problem. The easiest way is to delete the duplicates. But, that will also mean that some useful point events will be lost.

The second solution is use jittering, which will add a small perturbation to the duplicate points so that they do not occupy the exact same space.

The third solution is to make each point “unique” and then attach the duplicates of the points to the patterns as marks, as attributes of the points. Then you would need analytical techniques that take into account these marks.

The code chunk below implements the jittering approach.

childcare_ppp_jit <- rjitter(childcare_ppp, 
                             retry=TRUE, 
                             nsim=1, 
                             drop=TRUE)

DIY: Using the method you learned in previous section, check if any dusplicated point in this geospatial data.

any(duplicated(childcare_ppp_jit))

[1] FALSE

5.5.5 Creating owin object

When analysing spatial point patterns, it is a good practice to confine the analysis with a geographical area like Singapore boundary. In spatstat, an object called owin is specially designed to represent this polygonal region.

The code chunk below is used to covert sg SpatialPolygon object into owin object of spatstat.

sg_owin <- as(sg_sp, "owin")

The ouput object can be displayed by using plot() function

plot(sg_owin)

and summary() function of Base R.

summary(sg_owin)

Window: polygonal boundary
80 separate polygons (35 holes)
                  vertices         area relative.area
polygon 1                4  9.47108e+01      1.21e-07
polygon 2               37  1.29481e+04      1.66e-05
polygon 3               30  4.28933e+03      5.49e-06
polygon 4              145  9.61782e+05      1.23e-03
polygon 5              227  1.10308e+06      1.41e-03
polygon 6               19  3.09221e+04      3.95e-05
polygon 7               10  6.60195e+03      8.44e-06
polygon 8              234  2.08755e+06      2.67e-03
polygon 9               22  6.74651e+03      8.63e-06
polygon 10              71  5.63061e+03      7.20e-06
polygon 11              10  1.99717e+02      2.55e-07
polygon 12           14663  6.97996e+08      8.93e-01
polygon 13 (hole)        3 -2.05920e-03     -2.63e-12
polygon 14 (hole)        3 -2.89050e-05     -3.70e-14
polygon 15 (hole)        3 -2.83151e-01     -3.62e-10
polygon 16 (hole)        3 -3.99521e-02     -5.11e-11
polygon 17 (hole)        3 -4.95057e-02     -6.33e-11
polygon 18 (hole)        3 -3.65501e-03     -4.67e-12
polygon 19 (hole)        4 -2.05611e-02     -2.63e-11
polygon 20 (hole)        3 -1.68316e-04     -2.15e-13
polygon 21 (hole)       26 -1.25665e+03     -1.61e-06
polygon 22 (hole)        3 -2.18000e-06     -2.79e-15
polygon 23 (hole)        3 -6.62377e-01     -8.47e-10
polygon 24 (hole)        3 -2.09065e-03     -2.67e-12
polygon 25 (hole)       36 -7.79904e+03     -9.97e-06
polygon 26 (hole)        3 -8.83647e-03     -1.13e-11
polygon 27 (hole)        3 -2.21090e+00     -2.83e-09
polygon 28 (hole)       40 -6.00381e+03     -7.68e-06
polygon 29 (hole)        7 -1.40545e-01     -1.80e-10
polygon 30 (hole)       20 -4.39069e+00     -5.62e-09
polygon 31 (hole)       28 -1.99862e+01     -2.56e-08
polygon 32 (hole)       48 -1.38338e+02     -1.77e-07
polygon 33 (hole)      351 -1.21433e+03     -1.55e-06
polygon 34 (hole)       12 -8.36709e+01     -1.07e-07
polygon 35 (hole)      317 -5.11280e+04     -6.54e-05
polygon 36 (hole)       36 -4.01660e+04     -5.14e-05
polygon 37              30  2.80002e+04      3.58e-05
polygon 38              27  1.50315e+04      1.92e-05
polygon 39              15  4.03300e+04      5.16e-05
polygon 40            1045  4.44510e+06      5.68e-03
polygon 41 (hole)       13 -3.91907e+02     -5.01e-07
polygon 42              47  3.82087e+04      4.89e-05
polygon 43              65  8.42861e+04      1.08e-04
polygon 44             478  2.06120e+06      2.64e-03
polygon 45             266  1.50631e+06      1.93e-03
polygon 46             234  4.72886e+05      6.05e-04
polygon 47              14  5.86546e+03      7.50e-06
polygon 48              83  5.28920e+03      6.76e-06
polygon 49              75  1.73526e+04      2.22e-05
polygon 50             148  3.10395e+03      3.97e-06
polygon 51             142  3.22293e+03      4.12e-06
polygon 52              45  2.51218e+03      3.21e-06
polygon 53              40  1.38607e+04      1.77e-05
polygon 54              10  4.90942e+02      6.28e-07
polygon 55              95  5.96187e+04      7.62e-05
polygon 56 (hole)        4 -1.86410e-02     -2.38e-11
polygon 57              64  3.43149e+04      4.39e-05
polygon 58 (hole)        3 -1.98390e-03     -2.54e-12
polygon 59 (hole)        3 -5.55856e-03     -7.11e-12
polygon 60 (hole)        3 -5.12482e-03     -6.55e-12
polygon 61 (hole)        3 -1.96410e-03     -2.51e-12
polygon 62 (hole)        4 -1.13774e-02     -1.46e-11
polygon 63             155  2.67502e+05      3.42e-04
polygon 64             106  3.04104e+03      3.89e-06
polygon 65            1027  1.27782e+06      1.63e-03
polygon 66 (hole)        3 -3.23310e-04     -4.13e-13
polygon 67 (hole)        3 -1.16959e-03     -1.50e-12
polygon 68 (hole)        3 -1.46474e-03     -1.87e-12
polygon 69             211  4.70521e+05      6.02e-04
polygon 70               4  2.69313e+02      3.44e-07
polygon 71             132  9.53357e+04      1.22e-04
polygon 72               6  4.50259e+02      5.76e-07
polygon 73             285  1.61128e+06      2.06e-03
polygon 74              91  1.49663e+04      1.91e-05
polygon 75              71  8.18750e+03      1.05e-05
polygon 76             668  5.40368e+07      6.91e-02
polygon 77              77  3.29939e+05      4.22e-04
polygon 78             711  1.28815e+07      1.65e-02
polygon 79 (hole)        3 -3.41405e-01     -4.37e-10
polygon 80              44  2.26577e+03      2.90e-06
enclosing rectangle: [2667.54, 56396.44] x [15748.72, 50256.33] units
                     (53730 x 34510 units)
Window area = 781945000 square units
Fraction of frame area: 0.422

5.5.6 Combining point events object and owin object

In this last step of geospatial data wrangling, we will extract childcare events that are located within Singapore by using the code chunk below.

childcareSG_ppp = childcare_ppp[sg_owin]

The output object combined both the point and polygon feature in one ppp object class as shown below.

summary(childcareSG_ppp)

Planar point pattern:  1925 points
Average intensity 2.461811e-06 points per square unit

*Pattern contains duplicated points*

Coordinates are given to 3 decimal places
i.e. rounded to the nearest multiple of 0.001 units

Window: polygonal boundary
80 separate polygons (35 holes)
                  vertices         area relative.area
polygon 1                4  9.47108e+01      1.21e-07
polygon 2               37  1.29481e+04      1.66e-05
polygon 3               30  4.28933e+03      5.49e-06
polygon 4              145  9.61782e+05      1.23e-03
polygon 5              227  1.10308e+06      1.41e-03
polygon 6               19  3.09221e+04      3.95e-05
polygon 7               10  6.60195e+03      8.44e-06
polygon 8              234  2.08755e+06      2.67e-03
polygon 9               22  6.74651e+03      8.63e-06
polygon 10              71  5.63061e+03      7.20e-06
polygon 11              10  1.99717e+02      2.55e-07
polygon 12           14663  6.97996e+08      8.93e-01
polygon 13 (hole)        3 -2.05920e-03     -2.63e-12
polygon 14 (hole)        3 -2.89050e-05     -3.70e-14
polygon 15 (hole)        3 -2.83151e-01     -3.62e-10
polygon 16 (hole)        3 -3.99521e-02     -5.11e-11
polygon 17 (hole)        3 -4.95057e-02     -6.33e-11
polygon 18 (hole)        3 -3.65501e-03     -4.67e-12
polygon 19 (hole)        4 -2.05611e-02     -2.63e-11
polygon 20 (hole)        3 -1.68316e-04     -2.15e-13
polygon 21 (hole)       26 -1.25665e+03     -1.61e-06
polygon 22 (hole)        3 -2.18000e-06     -2.79e-15
polygon 23 (hole)        3 -6.62377e-01     -8.47e-10
polygon 24 (hole)        3 -2.09065e-03     -2.67e-12
polygon 25 (hole)       36 -7.79904e+03     -9.97e-06
polygon 26 (hole)        3 -8.83647e-03     -1.13e-11
polygon 27 (hole)        3 -2.21090e+00     -2.83e-09
polygon 28 (hole)       40 -6.00381e+03     -7.68e-06
polygon 29 (hole)        7 -1.40545e-01     -1.80e-10
polygon 30 (hole)       20 -4.39069e+00     -5.62e-09
polygon 31 (hole)       28 -1.99862e+01     -2.56e-08
polygon 32 (hole)       48 -1.38338e+02     -1.77e-07
polygon 33 (hole)      351 -1.21433e+03     -1.55e-06
polygon 34 (hole)       12 -8.36709e+01     -1.07e-07
polygon 35 (hole)      317 -5.11280e+04     -6.54e-05
polygon 36 (hole)       36 -4.01660e+04     -5.14e-05
polygon 37              30  2.80002e+04      3.58e-05
polygon 38              27  1.50315e+04      1.92e-05
polygon 39              15  4.03300e+04      5.16e-05
polygon 40            1045  4.44510e+06      5.68e-03
polygon 41 (hole)       13 -3.91907e+02     -5.01e-07
polygon 42              47  3.82087e+04      4.89e-05
polygon 43              65  8.42861e+04      1.08e-04
polygon 44             478  2.06120e+06      2.64e-03
polygon 45             266  1.50631e+06      1.93e-03
polygon 46             234  4.72886e+05      6.05e-04
polygon 47              14  5.86546e+03      7.50e-06
polygon 48              83  5.28920e+03      6.76e-06
polygon 49              75  1.73526e+04      2.22e-05
polygon 50             148  3.10395e+03      3.97e-06
polygon 51             142  3.22293e+03      4.12e-06
polygon 52              45  2.51218e+03      3.21e-06
polygon 53              40  1.38607e+04      1.77e-05
polygon 54              10  4.90942e+02      6.28e-07
polygon 55              95  5.96187e+04      7.62e-05
polygon 56 (hole)        4 -1.86410e-02     -2.38e-11
polygon 57              64  3.43149e+04      4.39e-05
polygon 58 (hole)        3 -1.98390e-03     -2.54e-12
polygon 59 (hole)        3 -5.55856e-03     -7.11e-12
polygon 60 (hole)        3 -5.12482e-03     -6.55e-12
polygon 61 (hole)        3 -1.96410e-03     -2.51e-12
polygon 62 (hole)        4 -1.13774e-02     -1.46e-11
polygon 63             155  2.67502e+05      3.42e-04
polygon 64             106  3.04104e+03      3.89e-06
polygon 65            1027  1.27782e+06      1.63e-03
polygon 66 (hole)        3 -3.23310e-04     -4.13e-13
polygon 67 (hole)        3 -1.16959e-03     -1.50e-12
polygon 68 (hole)        3 -1.46474e-03     -1.87e-12
polygon 69             211  4.70521e+05      6.02e-04
polygon 70               4  2.69313e+02      3.44e-07
polygon 71             132  9.53357e+04      1.22e-04
polygon 72               6  4.50259e+02      5.76e-07
polygon 73             285  1.61128e+06      2.06e-03
polygon 74              91  1.49663e+04      1.91e-05
polygon 75              71  8.18750e+03      1.05e-05
polygon 76             668  5.40368e+07      6.91e-02
polygon 77              77  3.29939e+05      4.22e-04
polygon 78             711  1.28815e+07      1.65e-02
polygon 79 (hole)        3 -3.41405e-01     -4.37e-10
polygon 80              44  2.26577e+03      2.90e-06
enclosing rectangle: [2667.54, 56396.44] x [15748.72, 50256.33] units
                     (53730 x 34510 units)
Window area = 781945000 square units
Fraction of frame area: 0.422

DIY: Using the method you learned in previous exercise, plot the newly derived childcareSG_ppp as shown below.

5.5.6.1 Extracting study area

The code chunk below will be used to extract the target planning areas.

pg = mpsz[mpsz@data$PLN_AREA_N == "PUNGGOL",]
tm = mpsz[mpsz@data$PLN_AREA_N == "TAMPINES",]
ck = mpsz[mpsz@data$PLN_AREA_N == "CHOA CHU KANG",]
jw = mpsz[mpsz@data$PLN_AREA_N == "JURONG WEST",]

Plotting target planning areas

par(mfrow=c(2,2))
plot(pg, main = "Ponggol")
plot(tm, main = "Tampines")
plot(ck, main = "Choa Chu Kang")
plot(jw, main = "Jurong West")

5.5.6.2 Converting the spatial point data frame into generic sp format

Next, we will convert these SpatialPolygonsDataFrame layers into generic spatialpolygons layers.

pg_sp = as(pg, "SpatialPolygons")
tm_sp = as(tm, "SpatialPolygons")
ck_sp = as(ck, "SpatialPolygons")
jw_sp = as(jw, "SpatialPolygons")

5.5.6.3 Creating owin object

Now, we will convert these SpatialPolygons objects into owin objects that is required by spatstat.

pg_owin = as(pg_sp, "owin")
tm_owin = as(tm_sp, "owin")
ck_owin = as(ck_sp, "owin")
jw_owin = as(jw_sp, "owin")

5.5.6.4 Combining childcare points and the study area

By using the code chunk below, we are able to extract childcare that is within the specific region to do our analysis later on.

childcare_pg_ppp = childcare_ppp_jit[pg_owin]
childcare_tm_ppp = childcare_ppp_jit[tm_owin]
childcare_ck_ppp = childcare_ppp_jit[ck_owin]
childcare_jw_ppp = childcare_ppp_jit[jw_owin]

Next, rescale() function is used to trasnform the unit of measurement from metre to kilometre.

childcare_pg_ppp.km = rescale(childcare_pg_ppp, 1000, "km")
childcare_tm_ppp.km = rescale(childcare_tm_ppp, 1000, "km")
childcare_ck_ppp.km = rescale(childcare_ck_ppp, 1000, "km")
childcare_jw_ppp.km = rescale(childcare_jw_ppp, 1000, "km")

The code chunk below is used to plot these four study areas and the locations of the childcare centres.

par(mfrow=c(2,2))
plot(childcare_pg_ppp.km, main="Punggol")
plot(childcare_tm_ppp.km, main="Tampines")
plot(childcare_ck_ppp.km, main="Choa Chu Kang")
plot(childcare_jw_ppp.km, main="Jurong West")

5.6 Second-order Spatial Point Patterns Analysis

5.7 Analysing Spatial Point Process Using G-Function

The G function measures the distribution of the distances from an arbitrary event to its nearest event. In this section, you will learn how to compute G-function estimation by using Gest() of spatstat package. You will also learn how to perform monta carlo simulation test using envelope() of spatstat package.

5.7.1 Choa Chu Kang planning area

5.7.1.1 Computing G-function estimation

The code chunk below is used to compute G-function using Gest() of spatat package.

G_CK = Gest(childcare_ck_ppp, correction = "border")
plot(G_CK, xlim=c(0,500))

5.7.1.2 Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of childcare services at Choa Chu Kang are randomly distributed.

H1= The distribution of childcare services at Choa Chu Kang are not randomly distributed.

The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.

Monte Carlo test with G-fucntion

G_CK.csr <- envelope(childcare_ck_ppp, Gest, nsim = 999)

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

plot(G_CK.csr)

5.7.2 Tampines planning area

5.7.2.1 Computing G-function estimation

G_tm = Gest(childcare_tm_ppp, correction = "best")
plot(G_tm)

5.7.2.2 Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of childcare services at Tampines are randomly distributed.

H1= The distribution of childcare services at Tampines are not randomly distributed.

The null hypothesis will be rejected is p-value is smaller than alpha value of 0.001.

The code chunk below is used to perform the hypothesis testing.

G_tm.csr <- envelope(childcare_tm_ppp, Gest, correction = "all", nsim = 999)

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

plot(G_tm.csr)

5.8 Analysing Spatial Point Process Using F-Function

The F function estimates the empty space function F(r) or its hazard rate h(r) from a point pattern in a window of arbitrary shape. In this section, you will learn how to compute F-function estimation by using Fest() of spatstat package. You will also learn how to perform monta carlo simulation test using envelope() of spatstat package.

5.8.1 Choa Chu Kang planning area

5.8.1.1 Computing F-function estimation

The code chunk below is used to compute F-function using Fest() of spatat package.

F_CK = Fest(childcare_ck_ppp)
plot(F_CK)

5.8.2 Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of childcare services at Choa Chu Kang are randomly distributed.

H1= The distribution of childcare services at Choa Chu Kang are not randomly distributed.

The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.

Monte Carlo test with F-function

F_CK.csr <- envelope(childcare_ck_ppp, Fest, nsim = 999)

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

plot(F_CK.csr)

5.8.3 Tampines planning area

5.8.3.1 Computing F-function estimation

Monte Carlo test with F-fucntion

F_tm = Fest(childcare_tm_ppp, correction = "best")
plot(F_tm)

5.8.3.2 Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of childcare services at Tampines are randomly distributed.

H1= The distribution of childcare services at Tampines are not randomly distributed.

The null hypothesis will be rejected is p-value is smaller than alpha value of 0.001.

The code chunk below is used to perform the hypothesis testing.

F_tm.csr <- envelope(childcare_tm_ppp, Fest, correction = "all", nsim = 999)

Generating 999 simulations of CSR  ...
1, 2, 3, ......10.........20.........30.........40.........50.........60..
.......70.........80.........90.........100.........110.........120.........130
.........140.........150.........160.........170.........180.........190........
.200.........210.........220.........230.........240.........250.........260......
...270.........280.........290.........300.........310.........320.........330....
.....340.........350.........360.........370.........380.........390.........400..
.......410.........420.........430.........440.........450.........460.........470
.........480.........490.........500.........510.........520.........530........
.540.........550.........560.........570.........580.........590.........600......
...610.........620.........630.........640.........650.........660.........670....
.....680.........690.........700.........710.........720.........730.........740..
.......750.........760.........770.........780.........790.........800.........810
.........820.........830.........840.........850.........860.........870........
.880.........890.........900.........910.........920.........930.........940......
...950.........960.........970.........980.........990........
999.

Done.

Done.

plot(F_tm.csr)

5.9 Analysing Spatial Point Process Using K-Function

K-function measures the number of events found up to a given distance of any particular event. In this section, you will learn how to compute K-function estimates by using Kest() of spatstat package. You will also learn how to perform monta carlo simulation test using envelope() of spatstat package.

5.9.1 Choa Chu Kang planning area

5.9.1.1 Computing K-function estimate

K_ck = Kest(childcare_ck_ppp, correction = "Ripley")
plot(K_ck, . -r ~ r, ylab= "K(d)-r", xlab = "d(m)")

5.9.1.2 Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of childcare services at Choa Chu Kang are randomly distributed.

H1= The distribution of childcare services at Choa Chu Kang are not randomly distributed.

The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.

The code chunk below is used to perform the hypothesis testing.

K_ck.csr <- envelope(childcare_ck_ppp, Kest, nsim = 99, rank = 1, glocal=TRUE)

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

plot(K_ck.csr, . - r ~ r, xlab="d", ylab="K(d)-r")

5.9.2 Tampines planning area

5.9.2.1 Computing K-function estimation

K_tm = Kest(childcare_tm_ppp, correction = "Ripley")
plot(K_tm, . -r ~ r, 
     ylab= "K(d)-r", xlab = "d(m)", 
     xlim=c(0,1000))

5.9.2.2 Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of childcare services at Tampines are randomly distributed.

K_tm.csr <- envelope(childcare_tm_ppp, Kest, nsim = 99, rank = 1, glocal=TRUE)

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

H1= The distribution of childcare services at Tampines are not randomly distributed.

The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.

The code chunk below is used to perform the hypothesis testing.

plot(K_tm.csr, . - r ~ r, 
     xlab="d", ylab="K(d)-r", xlim=c(0,500))

5.10 Analysing Spatial Point Process Using L-Function

In this section, you will learn how to compute L-function estimation by using Lest() of spatstat package. You will also learn how to perform monta carlo simulation test using envelope() of spatstat package.

5.10.1 Choa Chu Kang planning area

5.10.1.1 Computing L Fucntion estimation

L_ck = Lest(childcare_ck_ppp, correction = "Ripley")
plot(L_ck, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)")

5.10.1.2 Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of childcare services at Choa Chu Kang are randomly distributed.

H1= The distribution of childcare services at Choa Chu Kang are not randomly distributed.

The null hypothesis will be rejected if p-value if smaller than alpha value of 0.001.

The code chunk below is used to perform the hypothesis testing.

L_ck.csr <- envelope(childcare_ck_ppp, Lest, nsim = 99, rank = 1, glocal=TRUE)

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

plot(L_ck.csr, . - r ~ r, xlab="d", ylab="L(d)-r")

5.10.2 Tampines planning area

5.10.2.1 Computing L-function estimate

L_tm = Lest(childcare_tm_ppp, correction = "Ripley")
plot(L_tm, . -r ~ r, 
     ylab= "L(d)-r", xlab = "d(m)", 
     xlim=c(0,1000))

5.10.2.2 Performing Complete Spatial Randomness Test

To confirm the observed spatial patterns above, a hypothesis test will be conducted. The hypothesis and test are as follows:

Ho = The distribution of childcare services at Tampines are randomly distributed.

H1= The distribution of childcare services at Tampines are not randomly distributed.

The null hypothesis will be rejected if p-value is smaller than alpha value of 0.001.

The code chunk below will be used to perform the hypothesis testing.

L_tm.csr <- envelope(childcare_tm_ppp, Lest, nsim = 99, rank = 1, glocal=TRUE)

Generating 99 simulations of CSR  ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 
99.

Done.

Then, plot the model output by using the code chunk below.

plot(L_tm.csr, . - r ~ r, 
     xlab="d", ylab="L(d)-r", xlim=c(0,500))